2x-7=2/3x+10

Solution for 2x-7=2/3x+10 equation:

2x-7=2/3x+10

We move all terms to the left:

2x-7-(2/3x+10)=0


Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

2x-2/3x-10-7=0

We multiply all the terms by the denominator


2x*3x-10*3x-7*3x-2=0

Wy multiply elements

6x^2-30x-21x-2=0

We add all the numbers together, and all the variables

6x^2-51x-2=0

a = 6; b = -51; c = -2;
Δ = b2-4ac
Δ = -512-4·6·(-2)
Δ = 2649
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{-(-51)-\sqrt{2649}}{2*6}=\frac{51-\sqrt{2649}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2649}}{2*6}=\frac{51+\sqrt{2649}}{12}
$