3/2x-8=x+7+x

Solution for 3/2x-8=x+7+x equation:

3/2x-8=x+7+x

We move all terms to the left:

3/2x-8-(x+7+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(2x+7)-8=0

We get rid of parentheses

3/2x-2x-7-8=0

We multiply all the terms by the denominator


-2x*2x-7*2x-8*2x+3=0

Wy multiply elements

-4x^2-14x-16x+3=0

We add all the numbers together, and all the variables

-4x^2-30x+3=0

a = -4; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-4)·3
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*-4}=\frac{30-2\sqrt{237}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*-4}=\frac{30+2\sqrt{237}}{-8}
$