X+2/3(z)=90

Solution for X+2/3(z)=90 equation:

X+2/3(X)=90

We move all terms to the left:

X+2/3(X)-(90)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-90*3X+2=0

Wy multiply elements

3X^2-270X+2=0

a = 3; b = -270; c = +2;
Δ = b2-4ac
Δ = -2702-4·3·2
Δ = 72876
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:

$\sqrt{\Delta}=\sqrt{72876}=\sqrt{4*18219}=\sqrt{4}*\sqrt{18219}=2\sqrt{18219}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18219}}{2*3}=\frac{270-2\sqrt{18219}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18219}}{2*3}=\frac{270+2\sqrt{18219}}{6}
$