(7x-5)(6x+13)=180

Solution for (7x-5)(6x+13)=180 equation:

(7x-5)(6x+13)=180

We move all terms to the left:

(7x-5)(6x+13)-(180)=0

We multiply parentheses ..

(+42x^2+91x-30x-65)-180=0

We get rid of parentheses

42x^2+91x-30x-65-180=0

We add all the numbers together, and all the variables

42x^2+61x-245=0

a = 42; b = 61; c = -245;
Δ = b2-4ac
Δ = 612-4·42·(-245)
Δ = 44881
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{-(61)-\sqrt{44881}}{2*42}=\frac{-61-\sqrt{44881}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+\sqrt{44881}}{2*42}=\frac{-61+\sqrt{44881}}{84}
$