6x^2-17x+13=20^2-32

Solution for 6x^2-17x+13=20^2-32 equation:

6x^2-17x+13=20^2-32

We move all terms to the left:

6x^2-17x+13-(20^2-32)=0

We add all the numbers together, and all the variables

6x^2-17x-355=0

a = 6; b = -17; c = -355;
Δ = b2-4ac
Δ = -172-4·6·(-355)
Δ = 8809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{8809}}{2*6}=\frac{17-\sqrt{8809}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{8809}}{2*6}=\frac{17+\sqrt{8809}}{12}
$