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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x-5*2x-1*2x+7=0

Wy multiply elements

4x^2-10x-2x+7=0

We add all the numbers together, and all the variables

4x^2-12x+7=0

a = 4; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·4·7
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2}}{2*4}=\frac{12-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2}}{2*4}=\frac{12+4\sqrt{2}}{8}
$