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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


16x^2/72x^2+54x/72x^2+36x/72x^2-5=0

We multiply all the terms by the denominator


16x^2+54x+36x-5*72x^2=0

We add all the numbers together, and all the variables

16x^2+90x-5*72x^2=0

Wy multiply elements

16x^2-360x^2+90x=0

We add all the numbers together, and all the variables

-344x^2+90x=0

a = -344; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-344)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-344}=\frac{-180}{-688}
=45/172
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-344}=\frac{0}{-688}
=0
$