5/4x-3=2/3x+20

Solution for 5/4x-3=2/3x+20 equation:

5/4x-3=2/3x+20

We move all terms to the left:

5/4x-3-(2/3x+20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+20)!=0

x∈R


We get rid of parentheses

5/4x-2/3x-20-3=0

We calculate fractions


15x/12x^2+(-8x)/12x^2-20-3=0

We add all the numbers together, and all the variables

15x/12x^2+(-8x)/12x^2-23=0

We multiply all the terms by the denominator


15x+(-8x)-23*12x^2=0

Wy multiply elements

-276x^2+15x+(-8x)=0

We get rid of parentheses

-276x^2+15x-8x=0

We add all the numbers together, and all the variables

-276x^2+7x=0

a = -276; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-276)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-276}=\frac{-14}{-552}
=7/276
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-276}=\frac{0}{-552}
=0
$