(5x+2)(26x-8)=180

Solution for (5x+2)(26x-8)=180 equation:

(5x+2)(26x-8)=180

We move all terms to the left:

(5x+2)(26x-8)-(180)=0

We multiply parentheses ..

(+130x^2-40x+52x-16)-180=0

We get rid of parentheses

130x^2-40x+52x-16-180=0

We add all the numbers together, and all the variables

130x^2+12x-196=0

a = 130; b = 12; c = -196;
Δ = b2-4ac
Δ = 122-4·130·(-196)
Δ = 102064
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:

$\sqrt{\Delta}=\sqrt{102064}=\sqrt{16*6379}=\sqrt{16}*\sqrt{6379}=4\sqrt{6379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6379}}{2*130}=\frac{-12-4\sqrt{6379}}{260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6379}}{2*130}=\frac{-12+4\sqrt{6379}}{260}
$