(X+10)(13x-4)=90

Solution for (X+10)(13x-4)=90 equation:

(X+10)(13X-4)=90

We move all terms to the left:

(X+10)(13X-4)-(90)=0

We multiply parentheses ..

(+13X^2-4X+130X-40)-90=0

We get rid of parentheses

13X^2-4X+130X-40-90=0

We add all the numbers together, and all the variables

13X^2+126X-130=0

a = 13; b = 126; c = -130;
Δ = b2-4ac
Δ = 1262-4·13·(-130)
Δ = 22636
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:

$\sqrt{\Delta}=\sqrt{22636}=\sqrt{4*5659}=\sqrt{4}*\sqrt{5659}=2\sqrt{5659}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{5659}}{2*13}=\frac{-126-2\sqrt{5659}}{26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{5659}}{2*13}=\frac{-126+2\sqrt{5659}}{26}
$