(26x-4)(15x+29)=180

Solution for (26x-4)(15x+29)=180 equation:

(26x-4)(15x+29)=180

We move all terms to the left:

(26x-4)(15x+29)-(180)=0

We multiply parentheses ..

(+390x^2+754x-60x-116)-180=0

We get rid of parentheses

390x^2+754x-60x-116-180=0

We add all the numbers together, and all the variables

390x^2+694x-296=0

a = 390; b = 694; c = -296;
Δ = b2-4ac
Δ = 6942-4·390·(-296)
Δ = 943396
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:

$\sqrt{\Delta}=\sqrt{943396}=\sqrt{4*235849}=\sqrt{4}*\sqrt{235849}=2\sqrt{235849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(694)-2\sqrt{235849}}{2*390}=\frac{-694-2\sqrt{235849}}{780}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(694)+2\sqrt{235849}}{2*390}=\frac{-694+2\sqrt{235849}}{780}
$