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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-80x^2)/80x^2+32x/80x^2+(-60x)/80x^2-5=0

We multiply all the terms by the denominator


(-80x^2)+32x+(-60x)-5*80x^2=0

Wy multiply elements

(-80x^2)-400x^2+32x+(-60x)=0

We get rid of parentheses

-80x^2-400x^2+32x-60x=0

We add all the numbers together, and all the variables

-480x^2-28x=0

a = -480; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-480)·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*-480}=\frac{0}{-960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-480}=\frac{56}{-960}
=-7/120
$