X+40+2/3x=90

Solution for X+40+2/3x=90 equation:

X+40+2/3X=90

We move all terms to the left:

X+40+2/3X-(90)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X+2/3X-50=0

We multiply all the terms by the denominator


X*3X-50*3X+2=0

Wy multiply elements

3X^2-150X+2=0

a = 3; b = -150; c = +2;
Δ = b2-4ac
Δ = -1502-4·3·2
Δ = 22476
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:

$\sqrt{\Delta}=\sqrt{22476}=\sqrt{4*5619}=\sqrt{4}*\sqrt{5619}=2\sqrt{5619}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5619}}{2*3}=\frac{150-2\sqrt{5619}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5619}}{2*3}=\frac{150+2\sqrt{5619}}{6}
$