(5x-13)(8x-2)=180

Solution for (5x-13)(8x-2)=180 equation:

(5x-13)(8x-2)=180

We move all terms to the left:

(5x-13)(8x-2)-(180)=0

We multiply parentheses ..

(+40x^2-10x-104x+26)-180=0

We get rid of parentheses

40x^2-10x-104x+26-180=0

We add all the numbers together, and all the variables

40x^2-114x-154=0

a = 40; b = -114; c = -154;
Δ = b2-4ac
Δ = -1142-4·40·(-154)
Δ = 37636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{37636}=194$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-194}{2*40}=\frac{-80}{80}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+194}{2*40}=\frac{308}{80}
=3+17/20
$