1/2x=5/8x-7

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

1/2x=5/8x-7

We move all terms to the left:

1/2x-(5/8x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/16x^2+(-10x)/16x^2+7=0

We multiply all the terms by the denominator


8x+(-10x)+7*16x^2=0

Wy multiply elements

112x^2+8x+(-10x)=0

We get rid of parentheses

112x^2+8x-10x=0

We add all the numbers together, and all the variables

112x^2-2x=0

a = 112; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·112·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*112}=\frac{0}{224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*112}=\frac{4}{224}
=1/56
$