2/3x-3/4=-1/2x+5

Solution for 2/3x-3/4=-1/2x+5 equation:

2/3x-3/4=-1/2x+5

We move all terms to the left:

2/3x-3/4-(-1/2x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

2/3x+1/2x-5-3/4=0

We calculate fractions


(-36x^2)/96x^2+64x/96x^2+48x/96x^2-5=0

We multiply all the terms by the denominator


(-36x^2)+64x+48x-5*96x^2=0

We add all the numbers together, and all the variables

(-36x^2)+112x-5*96x^2=0

Wy multiply elements

(-36x^2)-480x^2+112x=0

We get rid of parentheses

-36x^2-480x^2+112x=0

We add all the numbers together, and all the variables

-516x^2+112x=0

a = -516; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·(-516)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*-516}=\frac{-224}{-1032}
=28/129
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*-516}=\frac{0}{-1032}
=0
$