12x-3/2x=x+10

Solution for 12x-3/2x=x+10 equation:

12x-3/2x=x+10

We move all terms to the left:

12x-3/2x-(x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

12x-3/2x-x-10=0

We multiply all the terms by the denominator


12x*2x-x*2x-10*2x-3=0

Wy multiply elements

24x^2-2x^2-20x-3=0

We add all the numbers together, and all the variables

22x^2-20x-3=0

a = 22; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·22·(-3)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{166}}{2*22}=\frac{20-2\sqrt{166}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{166}}{2*22}=\frac{20+2\sqrt{166}}{44}
$