(10x-13)(x+6)=180

Solution for (10x-13)(x+6)=180 equation:

(10x-13)(x+6)=180

We move all terms to the left:

(10x-13)(x+6)-(180)=0

We multiply parentheses ..

(+10x^2+60x-13x-78)-180=0

We get rid of parentheses

10x^2+60x-13x-78-180=0

We add all the numbers together, and all the variables

10x^2+47x-258=0

a = 10; b = 47; c = -258;
Δ = b2-4ac
Δ = 472-4·10·(-258)
Δ = 12529
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{-(47)-\sqrt{12529}}{2*10}=\frac{-47-\sqrt{12529}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{12529}}{2*10}=\frac{-47+\sqrt{12529}}{20}
$