90=(2/3x+4)x

Solution for 90=(2/3x+4)x equation:

90=(2/3x+4)x

We move all terms to the left:

90-((2/3x+4)x)=0


Domain of the equation: 3x+4)x)!=0

x∈R


We multiply all the terms by the denominator


-((2+90*3x+4)x)=0


We calculate terms in parentheses: -((2+90*3x+4)x), so:

(2+90*3x+4)x

We add all the numbers together, and all the variables

(90*3x+6)x

We multiply parentheses

270x^2+6x

Back to the equation:

-(270x^2+6x)


We get rid of parentheses

-270x^2-6x=0

a = -270; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-270)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-270}=\frac{0}{-540}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-270}=\frac{12}{-540}
=-1/45
$