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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

12x^2-48x-3=0

a = 12; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·12·(-3)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{17}}{2*12}=\frac{48-12\sqrt{17}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{17}}{2*12}=\frac{48+12\sqrt{17}}{24}
$