1/5x-3/8=3/2x+2

Solution for 1/5x-3/8=3/2x+2 equation:

1/5x-3/8=3/2x+2

We move all terms to the left:

1/5x-3/8-(3/2x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-3/2x-2-3/8=0

We calculate fractions


(-60x^2)/640x^2+128x/640x^2+(-960x)/640x^2-2=0

We multiply all the terms by the denominator


(-60x^2)+128x+(-960x)-2*640x^2=0

Wy multiply elements

(-60x^2)-1280x^2+128x+(-960x)=0

We get rid of parentheses

-60x^2-1280x^2+128x-960x=0

We add all the numbers together, and all the variables

-1340x^2-832x=0

a = -1340; b = -832; c = 0;
Δ = b2-4ac
Δ = -8322-4·(-1340)·0
Δ = 692224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{692224}=832$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-832)-832}{2*-1340}=\frac{0}{-2680}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-832)+832}{2*-1340}=\frac{1664}{-2680}
=-208/335
$