(9x+5)(10x-2)=180

Solution for (9x+5)(10x-2)=180 equation:

(9x+5)(10x-2)=180

We move all terms to the left:

(9x+5)(10x-2)-(180)=0

We multiply parentheses ..

(+90x^2-18x+50x-10)-180=0

We get rid of parentheses

90x^2-18x+50x-10-180=0

We add all the numbers together, and all the variables

90x^2+32x-190=0

a = 90; b = 32; c = -190;
Δ = b2-4ac
Δ = 322-4·90·(-190)
Δ = 69424
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:

$\sqrt{\Delta}=\sqrt{69424}=\sqrt{16*4339}=\sqrt{16}*\sqrt{4339}=4\sqrt{4339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{4339}}{2*90}=\frac{-32-4\sqrt{4339}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{4339}}{2*90}=\frac{-32+4\sqrt{4339}}{180}
$