(5x-7)(9x+19)=180

Solution for (5x-7)(9x+19)=180 equation:

(5x-7)(9x+19)=180

We move all terms to the left:

(5x-7)(9x+19)-(180)=0

We multiply parentheses ..

(+45x^2+95x-63x-133)-180=0

We get rid of parentheses

45x^2+95x-63x-133-180=0

We add all the numbers together, and all the variables

45x^2+32x-313=0

a = 45; b = 32; c = -313;
Δ = b2-4ac
Δ = 322-4·45·(-313)
Δ = 57364
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:

$\sqrt{\Delta}=\sqrt{57364}=\sqrt{4*14341}=\sqrt{4}*\sqrt{14341}=2\sqrt{14341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{14341}}{2*45}=\frac{-32-2\sqrt{14341}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{14341}}{2*45}=\frac{-32+2\sqrt{14341}}{90}
$