-3/4x-20=5/6x+31

Solution for -3/4x-20=5/6x+31 equation:

-3/4x-20=5/6x+31

We move all terms to the left:

-3/4x-20-(5/6x+31)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+31)!=0

x∈R


We get rid of parentheses

-3/4x-5/6x-31-20=0

We calculate fractions


(-18x)/24x^2+(-20x)/24x^2-31-20=0

We add all the numbers together, and all the variables

(-18x)/24x^2+(-20x)/24x^2-51=0

We multiply all the terms by the denominator


(-18x)+(-20x)-51*24x^2=0

Wy multiply elements

-1224x^2+(-18x)+(-20x)=0

We get rid of parentheses

-1224x^2-18x-20x=0

We add all the numbers together, and all the variables

-1224x^2-38x=0

a = -1224; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·(-1224)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*-1224}=\frac{0}{-2448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*-1224}=\frac{76}{-2448}
=-19/612
$