(x+8)(6x-58)=20

Solution for (x+8)(6x-58)=20 equation:

(x+8)(6x-58)=20

We move all terms to the left:

(x+8)(6x-58)-(20)=0

We multiply parentheses ..

(+6x^2-58x+48x-464)-20=0

We get rid of parentheses

6x^2-58x+48x-464-20=0

We add all the numbers together, and all the variables

6x^2-10x-484=0

a = 6; b = -10; c = -484;
Δ = b2-4ac
Δ = -102-4·6·(-484)
Δ = 11716
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:

$\sqrt{\Delta}=\sqrt{11716}=\sqrt{4*2929}=\sqrt{4}*\sqrt{2929}=2\sqrt{2929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2929}}{2*6}=\frac{10-2\sqrt{2929}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2929}}{2*6}=\frac{10+2\sqrt{2929}}{12}
$