4/5x+12=3/4x+30

Solution for 4/5x+12=3/4x+30 equation:

4/5x+12=3/4x+30

We move all terms to the left:

4/5x+12-(3/4x+30)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+30)!=0

x∈R


We get rid of parentheses

4/5x-3/4x-30+12=0

We calculate fractions


16x/20x^2+(-15x)/20x^2-30+12=0

We add all the numbers together, and all the variables

16x/20x^2+(-15x)/20x^2-18=0

We multiply all the terms by the denominator


16x+(-15x)-18*20x^2=0

Wy multiply elements

-360x^2+16x+(-15x)=0

We get rid of parentheses

-360x^2+16x-15x=0

We add all the numbers together, and all the variables

-360x^2+x=0

a = -360; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-360)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-360}=\frac{-2}{-720}
=1/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-360}=\frac{0}{-720}
=0
$