(7x+23)(5x+19)=180

Solution for (7x+23)(5x+19)=180 equation:

(7x+23)(5x+19)=180

We move all terms to the left:

(7x+23)(5x+19)-(180)=0

We multiply parentheses ..

(+35x^2+133x+115x+437)-180=0

We get rid of parentheses

35x^2+133x+115x+437-180=0

We add all the numbers together, and all the variables

35x^2+248x+257=0

a = 35; b = 248; c = +257;
Δ = b2-4ac
Δ = 2482-4·35·257
Δ = 25524
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:

$\sqrt{\Delta}=\sqrt{25524}=\sqrt{36*709}=\sqrt{36}*\sqrt{709}=6\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(248)-6\sqrt{709}}{2*35}=\frac{-248-6\sqrt{709}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(248)+6\sqrt{709}}{2*35}=\frac{-248+6\sqrt{709}}{70}
$