X-8=-2/3x+7

Solution for X-8=-2/3x+7 equation:

X-8=-2/3X+7

We move all terms to the left:

X-8-(-2/3X+7)=0


Domain of the equation: 3X+7)!=0

X∈R


We get rid of parentheses

X+2/3X-7-8=0

We multiply all the terms by the denominator


X*3X-7*3X-8*3X+2=0

Wy multiply elements

3X^2-21X-24X+2=0

We add all the numbers together, and all the variables

3X^2-45X+2=0

a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6}
$