It looks like you've uploaded a math problem sheet containing quadratic equations. Let's start by solving each equation step by step. I'll begin with the first few and guide you through them.

a) $x^2 - 4x + 3 = 0$
This is a simple quadratic equation. To solve it, we can factor it.

$x^2 - 4x + 3 = (x - 1)(x - 3) = 0$

Setting each factor equal to zero:

$x - 1 = 0 \quad \text{or} \quad x - 3 = 0$

Thus, the solutions are:

$x = 1 \quad \text{or} \quad x = 3$

b) $2x^2 - 9x = 35$
First, move the 35 to the left-hand side:

$2x^2 - 9x - 35 = 0$

Now, we can try to factor this quadratic equation, or we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ For $2x^2 - 9x - 35 = 0$, $a = 2$, $b = -9$, and $c = -35$.

Substituting into the formula:

$x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(2)(-35)}}{2(2)} = \frac{9 \pm \sqrt{81 + 280}}{4} = \frac{9 \pm \sqrt{361}}{4} = \frac{9 \pm 19}{4}$

Thus, the two solutions are:

$x = \frac{9 + 19}{4} = \frac{28}{4} = 7 \quad \text{or} \quad x = \frac{9 - 19}{4} = \frac{-10}{4} = -2.5$

I'll continue solving the remaining equations step-by-step. Would you like me to go over more equations, or do you want a detailed explanation for any specific one from the list?