3/4x-12=7/8x-5

Solution for 3/4x-12=7/8x-5 equation:

3/4x-12=7/8x-5

We move all terms to the left:

3/4x-12-(7/8x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

3/4x-7/8x+5-12=0

We calculate fractions


24x/32x^2+(-28x)/32x^2+5-12=0

We add all the numbers together, and all the variables

24x/32x^2+(-28x)/32x^2-7=0

We multiply all the terms by the denominator


24x+(-28x)-7*32x^2=0

Wy multiply elements

-224x^2+24x+(-28x)=0

We get rid of parentheses

-224x^2+24x-28x=0

We add all the numbers together, and all the variables

-224x^2-4x=0

a = -224; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-224)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-224}=\frac{0}{-448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-224}=\frac{8}{-448}
=-1/56
$