X=2/3x-20

Solution for X=2/3x-20 equation:

X=2/3X-20

We move all terms to the left:

X-(2/3X-20)=0


Domain of the equation: 3X-20)!=0

X∈R


We get rid of parentheses

X-2/3X+20=0

We multiply all the terms by the denominator


X*3X+20*3X-2=0

Wy multiply elements

3X^2+60X-2=0

a = 3; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·3·(-2)
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{906}}{2*3}=\frac{-60-2\sqrt{906}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{906}}{2*3}=\frac{-60+2\sqrt{906}}{6}
$