90(15x+30)10x=180

Solution for 90(15x+30)10x=180 equation:

90(15x+30)10x=180

We move all terms to the left:

90(15x+30)10x-(180)=0

We multiply parentheses

13500x^2+27000x-180=0

a = 13500; b = 27000; c = -180;
Δ = b2-4ac
Δ = 270002-4·13500·(-180)
Δ = 738720000
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:

$\sqrt{\Delta}=\sqrt{738720000}=\sqrt{12960000*57}=\sqrt{12960000}*\sqrt{57}=3600\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27000)-3600\sqrt{57}}{2*13500}=\frac{-27000-3600\sqrt{57}}{27000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27000)+3600\sqrt{57}}{2*13500}=\frac{-27000+3600\sqrt{57}}{27000}
$