3/2x-8=x+7+1/2x

Solution for 3/2x-8=x+7+1/2x equation:

3/2x-8=x+7+1/2x

We move all terms to the left:

3/2x-8-(x+7+1/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(x+1/2x+7)-8=0

We get rid of parentheses

3/2x-x-1/2x-7-8=0

We multiply all the terms by the denominator


-x*2x-7*2x-8*2x+3-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-2)·2
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*-2}=\frac{30-2\sqrt{229}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*-2}=\frac{30+2\sqrt{229}}{-4}
$