3/5x+7/8=1/2x-2

Solution for 3/5x+7/8=1/2x-2 equation:

3/5x+7/8=1/2x-2

We move all terms to the left:

3/5x+7/8-(1/2x-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

3/5x-1/2x+2+7/8=0

We calculate fractions


140x^2/640x^2+384x/640x^2+(-320x)/640x^2+2=0

We multiply all the terms by the denominator


140x^2+384x+(-320x)+2*640x^2=0

Wy multiply elements

140x^2+1280x^2+384x+(-320x)=0

We get rid of parentheses

140x^2+1280x^2+384x-320x=0

We add all the numbers together, and all the variables

1420x^2+64x=0

a = 1420; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·1420·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*1420}=\frac{-128}{2840}
=-16/355
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*1420}=\frac{0}{2840}
=0
$