2x+10=-2/3x+2

Solution for 2x+10=-2/3x+2 equation:

2x+10=-2/3x+2

We move all terms to the left:

2x+10-(-2/3x+2)=0


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

2x+2/3x-2+10=0

We multiply all the terms by the denominator


2x*3x-2*3x+10*3x+2=0

Wy multiply elements

6x^2-6x+30x+2=0

We add all the numbers together, and all the variables

6x^2+24x+2=0

a = 6; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·6·2
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*6}=\frac{-24-4\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*6}=\frac{-24+4\sqrt{33}}{12}
$