(7x-2)(8x-23)=180

Solution for (7x-2)(8x-23)=180 equation:

(7x-2)(8x-23)=180

We move all terms to the left:

(7x-2)(8x-23)-(180)=0

We multiply parentheses ..

(+56x^2-161x-16x+46)-180=0

We get rid of parentheses

56x^2-161x-16x+46-180=0

We add all the numbers together, and all the variables

56x^2-177x-134=0

a = 56; b = -177; c = -134;
Δ = b2-4ac
Δ = -1772-4·56·(-134)
Δ = 61345
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{-(-177)-\sqrt{61345}}{2*56}=\frac{177-\sqrt{61345}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+\sqrt{61345}}{2*56}=\frac{177+\sqrt{61345}}{112}
$