90=(3x+42)3x

Solution for 90=(3x+42)3x equation:

90=(3x+42)3x

We move all terms to the left:

90-((3x+42)3x)=0


We calculate terms in parentheses: -((3x+42)3x), so:

(3x+42)3x

We multiply parentheses

9x^2+126x

Back to the equation:

-(9x^2+126x)


We get rid of parentheses

-9x^2-126x+90=0

a = -9; b = -126; c = +90;
Δ = b2-4ac
Δ = -1262-4·(-9)·90
Δ = 19116
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:

$\sqrt{\Delta}=\sqrt{19116}=\sqrt{324*59}=\sqrt{324}*\sqrt{59}=18\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-18\sqrt{59}}{2*-9}=\frac{126-18\sqrt{59}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+18\sqrt{59}}{2*-9}=\frac{126+18\sqrt{59}}{-18}
$