X=91/3x-2

Solution for X=91/3x-2 equation:

X=91/3X-2

We move all terms to the left:

X-(91/3X-2)=0


Domain of the equation: 3X-2)!=0

X∈R


We get rid of parentheses

X-91/3X+2=0

We multiply all the terms by the denominator


X*3X+2*3X-91=0

Wy multiply elements

3X^2+6X-91=0

a = 3; b = 6; c = -91;
Δ = b2-4ac
Δ = 62-4·3·(-91)
Δ = 1128
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:

$\sqrt{\Delta}=\sqrt{1128}=\sqrt{4*282}=\sqrt{4}*\sqrt{282}=2\sqrt{282}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{282}}{2*3}=\frac{-6-2\sqrt{282}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{282}}{2*3}=\frac{-6+2\sqrt{282}}{6}
$