x-12+4/3x=90

Solution for x-12+4/3x=90 equation:

x-12+4/3x=90

We move all terms to the left:

x-12+4/3x-(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+4/3x-102=0

We multiply all the terms by the denominator


x*3x-102*3x+4=0

Wy multiply elements

3x^2-306x+4=0

a = 3; b = -306; c = +4;
Δ = b2-4ac
Δ = -3062-4·3·4
Δ = 93588
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:

$\sqrt{\Delta}=\sqrt{93588}=\sqrt{4*23397}=\sqrt{4}*\sqrt{23397}=2\sqrt{23397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-306)-2\sqrt{23397}}{2*3}=\frac{306-2\sqrt{23397}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-306)+2\sqrt{23397}}{2*3}=\frac{306+2\sqrt{23397}}{6}
$