3x-12=1/4x+10

Solution for 3x-12=1/4x+10 equation:

3x-12=1/4x+10

We move all terms to the left:

3x-12-(1/4x+10)=0


Domain of the equation: 4x+10)!=0

x∈R


We get rid of parentheses

3x-1/4x-10-12=0

We multiply all the terms by the denominator


3x*4x-10*4x-12*4x-1=0

Wy multiply elements

12x^2-40x-48x-1=0

We add all the numbers together, and all the variables

12x^2-88x-1=0

a = 12; b = -88; c = -1;
Δ = b2-4ac
Δ = -882-4·12·(-1)
Δ = 7792
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:

$\sqrt{\Delta}=\sqrt{7792}=\sqrt{16*487}=\sqrt{16}*\sqrt{487}=4\sqrt{487}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{487}}{2*12}=\frac{88-4\sqrt{487}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{487}}{2*12}=\frac{88+4\sqrt{487}}{24}
$