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3/2x-2=x+8

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



3/2x-2=x+8

We move all terms to the left:

3/2x-2-(x+8)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We get rid of parentheses

3/2x-x-8-2=0

We multiply all the terms by the denominator


-x*2x-8*2x-2*2x+3=0

Wy multiply elements

-2x^2-16x-4x+3=0

We add all the numbers together, and all the variables

-2x^2-20x+3=0

a = -2; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-2)·3
Δ = 424
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{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}


x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*-2}=\frac{20-2\sqrt{106}}{-4}



x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*-2}=\frac{20+2\sqrt{106}}{-4}

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