(2/3*x)=90

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

(2/3*x)=90

We move all terms to the left:

(2/3*x)-(90)=0


Domain of the equation: 3*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3*x-90=0

We multiply all the terms by the denominator


-90*3*x+2=0

Wy multiply elements

-270x*x+2=0

Wy multiply elements

-270x^2+2=0

a = -270; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-270)·2
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*-270}=\frac{0-12\sqrt{15}}{-540}
=-\frac{12\sqrt{15}}{-540}
=-\frac{\sqrt{15}}{-45}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*-270}=\frac{0+12\sqrt{15}}{-540}
=\frac{12\sqrt{15}}{-540}
=\frac{\sqrt{15}}{-45}
$