3x+12=3/4x+15

Solution for 3x+12=3/4x+15 equation:

3x+12=3/4x+15

We move all terms to the left:

3x+12-(3/4x+15)=0


Domain of the equation: 4x+15)!=0

x∈R


We get rid of parentheses

3x-3/4x-15+12=0

We multiply all the terms by the denominator


3x*4x-15*4x+12*4x-3=0

Wy multiply elements

12x^2-60x+48x-3=0

We add all the numbers together, and all the variables

12x^2-12x-3=0

a = 12; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·12·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*12}=\frac{12-12\sqrt{2}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*12}=\frac{12+12\sqrt{2}}{24}
$