3/4x-12=2.5x-40

Solution for 3/4x-12=2.5x-40 equation:

3/4x-12=2.5x-40

We move all terms to the left:

3/4x-12-(2.5x-40)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2.5x+40-12=0

We multiply all the terms by the denominator


-(2.5x)*4x+40*4x-12*4x+3=0

We add all the numbers together, and all the variables

-(+2.5x)*4x+40*4x-12*4x+3=0

We multiply parentheses

-8x^2+40*4x-12*4x+3=0

Wy multiply elements

-8x^2+160x-48x+3=0

We add all the numbers together, and all the variables

-8x^2+112x+3=0

a = -8; b = 112; c = +3;
Δ = b2-4ac
Δ = 1122-4·(-8)·3
Δ = 12640
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:

$\sqrt{\Delta}=\sqrt{12640}=\sqrt{16*790}=\sqrt{16}*\sqrt{790}=4\sqrt{790}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{790}}{2*-8}=\frac{-112-4\sqrt{790}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{790}}{2*-8}=\frac{-112+4\sqrt{790}}{-16}
$