7x^2-32x+13=0

Solution for 7x^2-32x+13=0 equation:

7x^2-32x+13=0

a = 7; b = -32; c = +13;
Δ = b2-4ac
Δ = -322-4·7·13
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{165}}{2*7}=\frac{32-2\sqrt{165}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{165}}{2*7}=\frac{32+2\sqrt{165}}{14}
$