3/4x+2=4/5x-7

Solution for 3/4x+2=4/5x-7 equation:

3/4x+2=4/5x-7

We move all terms to the left:

3/4x+2-(4/5x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

3/4x-4/5x+7+2=0

We calculate fractions


15x/20x^2+(-16x)/20x^2+7+2=0

We add all the numbers together, and all the variables

15x/20x^2+(-16x)/20x^2+9=0

We multiply all the terms by the denominator


15x+(-16x)+9*20x^2=0

Wy multiply elements

180x^2+15x+(-16x)=0

We get rid of parentheses

180x^2+15x-16x=0

We add all the numbers together, and all the variables

180x^2-1x=0

a = 180; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·180·0
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*180}=\frac{0}{360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*180}=\frac{2}{360}
=1/180
$