X-7=2/3x+5

Solution for X-7=2/3x+5 equation:

X-7=2/3X+5

We move all terms to the left:

X-7-(2/3X+5)=0


Domain of the equation: 3X+5)!=0

X∈R


We get rid of parentheses

X-2/3X-5-7=0

We multiply all the terms by the denominator


X*3X-5*3X-7*3X-2=0

Wy multiply elements

3X^2-15X-21X-2=0

We add all the numbers together, and all the variables

3X^2-36X-2=0

a = 3; b = -36; c = -2;
Δ = b2-4ac
Δ = -362-4·3·(-2)
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{330}}{2*3}=\frac{36-2\sqrt{330}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{330}}{2*3}=\frac{36+2\sqrt{330}}{6}
$