2x(3/2x+20)=90

Solution for 2x(3/2x+20)=90 equation:

2x(3/2x+20)=90

We move all terms to the left:

2x(3/2x+20)-(90)=0


Domain of the equation: 2x+20)!=0

x∈R


We multiply parentheses

6x^2+40x-90=0

a = 6; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·6·(-90)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{235}}{2*6}=\frac{-40-4\sqrt{235}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{235}}{2*6}=\frac{-40+4\sqrt{235}}{12}
$