12x-4=3/2x+5

Solution for 12x-4=3/2x+5 equation:

12x-4=3/2x+5

We move all terms to the left:

12x-4-(3/2x+5)=0


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

x∈R


We get rid of parentheses

12x-3/2x-5-4=0

We multiply all the terms by the denominator


12x*2x-5*2x-4*2x-3=0

Wy multiply elements

24x^2-10x-8x-3=0

We add all the numbers together, and all the variables

24x^2-18x-3=0

a = 24; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·24·(-3)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*24}=\frac{18-6\sqrt{17}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*24}=\frac{18+6\sqrt{17}}{48}
$