13x(-9x+20)=30+2

Solution for 13x(-9x+20)=30+2 equation:

13x(-9x+20)=30+2

We move all terms to the left:

13x(-9x+20)-(30+2)=0

We add all the numbers together, and all the variables

13x(-9x+20)-32=0

We multiply parentheses

-117x^2+260x-32=0

a = -117; b = 260; c = -32;
Δ = b2-4ac
Δ = 2602-4·(-117)·(-32)
Δ = 52624
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:

$\sqrt{\Delta}=\sqrt{52624}=\sqrt{16*3289}=\sqrt{16}*\sqrt{3289}=4\sqrt{3289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-4\sqrt{3289}}{2*-117}=\frac{-260-4\sqrt{3289}}{-234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+4\sqrt{3289}}{2*-117}=\frac{-260+4\sqrt{3289}}{-234}
$