X(2x-20)=-13

Solution for X(2x-20)=-13 equation:

X(2X-20)=-13

We move all terms to the left:

X(2X-20)-(-13)=0

We add all the numbers together, and all the variables

X(2X-20)+13=0

We multiply parentheses

2X^2-20X+13=0

a = 2; b = -20; c = +13;
Δ = b2-4ac
Δ = -202-4·2·13
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{74}}{2*2}=\frac{20-2\sqrt{74}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{74}}{2*2}=\frac{20+2\sqrt{74}}{4}
$