(5x-11)(8x-3)=180

Solution for (5x-11)(8x-3)=180 equation:

(5x-11)(8x-3)=180

We move all terms to the left:

(5x-11)(8x-3)-(180)=0

We multiply parentheses ..

(+40x^2-15x-88x+33)-180=0

We get rid of parentheses

40x^2-15x-88x+33-180=0

We add all the numbers together, and all the variables

40x^2-103x-147=0

a = 40; b = -103; c = -147;
Δ = b2-4ac
Δ = -1032-4·40·(-147)
Δ = 34129
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{-(-103)-\sqrt{34129}}{2*40}=\frac{103-\sqrt{34129}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-103)+\sqrt{34129}}{2*40}=\frac{103+\sqrt{34129}}{80}
$