(8x+19)(21x-13)=180

Solution for (8x+19)(21x-13)=180 equation:

(8x+19)(21x-13)=180

We move all terms to the left:

(8x+19)(21x-13)-(180)=0

We multiply parentheses ..

(+168x^2-104x+399x-247)-180=0

We get rid of parentheses

168x^2-104x+399x-247-180=0

We add all the numbers together, and all the variables

168x^2+295x-427=0

a = 168; b = 295; c = -427;
Δ = b2-4ac
Δ = 2952-4·168·(-427)
Δ = 373969
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{-(295)-\sqrt{373969}}{2*168}=\frac{-295-\sqrt{373969}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(295)+\sqrt{373969}}{2*168}=\frac{-295+\sqrt{373969}}{336}
$