(3x+5)2x=90

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

(3x+5)2x=90

We move all terms to the left:

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

We multiply 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}
$