90=(3x-5)2x

Solution for 90=(3x-5)2x equation:

90=(3x-5)2x

We move all terms to the left:

90-((3x-5)2x)=0


We calculate terms in parentheses: -((3x-5)2x), so:

(3x-5)2x

We multiply parentheses

6x^2-10x

Back to the equation:

-(6x^2-10x)


We get rid of parentheses

-6x^2+10x+90=0

a = -6; b = 10; c = +90;
Δ = b2-4ac
Δ = 102-4·(-6)·90
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{565}}{2*-6}=\frac{-10-2\sqrt{565}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{565}}{2*-6}=\frac{-10+2\sqrt{565}}{-12}
$