2x-12=3/2x+5

Solution for 2x-12=3/2x+5 equation:

2x-12=3/2x+5

We move all terms to the left:

2x-12-(3/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

2x-3/2x-5-12=0

We multiply all the terms by the denominator


2x*2x-5*2x-12*2x-3=0

Wy multiply elements

4x^2-10x-24x-3=0

We add all the numbers together, and all the variables

4x^2-34x-3=0

a = 4; b = -34; c = -3;
Δ = b2-4ac
Δ = -342-4·4·(-3)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{301}}{2*4}=\frac{34-2\sqrt{301}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{301}}{2*4}=\frac{34+2\sqrt{301}}{8}
$