-1/2x-7/2=8/4x-7

Solution for -1/2x-7/2=8/4x-7 equation:

-1/2x-7/2=8/4x-7

We move all terms to the left:

-1/2x-7/2-(8/4x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

-1/2x-8/4x+7-7/2=0

We calculate fractions


(-4x)/32x^2+(-64x)/32x^2+(-28x)/32x^2+7=0

We multiply all the terms by the denominator


(-4x)+(-64x)+(-28x)+7*32x^2=0

Wy multiply elements

224x^2+(-4x)+(-64x)+(-28x)=0

We get rid of parentheses

224x^2-4x-64x-28x=0

We add all the numbers together, and all the variables

224x^2-96x=0

a = 224; b = -96; c = 0;
Δ = b2-4ac
Δ = -962-4·224·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-96}{2*224}=\frac{0}{448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+96}{2*224}=\frac{192}{448}
=3/7
$