2x-7=2/3x+10

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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} $

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