3/2x-8=-x-5

Solution for 3/2x-8=-x-5 equation:

3/2x-8=-x-5

We move all terms to the left:

3/2x-8-(-x-5)=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-(-1x-5)-8=0

We get rid of parentheses

3/2x+1x+5-8=0

We multiply all the terms by the denominator


1x*2x+5*2x-8*2x+3=0

Wy multiply elements

2x^2+10x-16x+3=0

We add all the numbers together, and all the variables

2x^2-6x+3=0

a = 2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·2·3
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*2}=\frac{6-2\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*2}=\frac{6+2\sqrt{3}}{4}
$