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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-100x^2)/80x^2+60x/80x^2+(-32x)/80x^2-3=0

We multiply all the terms by the denominator


(-100x^2)+60x+(-32x)-3*80x^2=0

Wy multiply elements

(-100x^2)-240x^2+60x+(-32x)=0

We get rid of parentheses

-100x^2-240x^2+60x-32x=0

We add all the numbers together, and all the variables

-340x^2+28x=0

a = -340; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-340)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-340}=\frac{-56}{-680}
=7/85
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-340}=\frac{0}{-680}
=0
$