(8x-1)(5x+23)=180

Solution for (8x-1)(5x+23)=180 equation:

(8x-1)(5x+23)=180

We move all terms to the left:

(8x-1)(5x+23)-(180)=0

We multiply parentheses ..

(+40x^2+184x-5x-23)-180=0

We get rid of parentheses

40x^2+184x-5x-23-180=0

We add all the numbers together, and all the variables

40x^2+179x-203=0

a = 40; b = 179; c = -203;
Δ = b2-4ac
Δ = 1792-4·40·(-203)
Δ = 64521
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:

$\sqrt{\Delta}=\sqrt{64521}=\sqrt{9*7169}=\sqrt{9}*\sqrt{7169}=3\sqrt{7169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(179)-3\sqrt{7169}}{2*40}=\frac{-179-3\sqrt{7169}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(179)+3\sqrt{7169}}{2*40}=\frac{-179+3\sqrt{7169}}{80}
$