x+1/2x-5=4x-7/2x+5

Solution for x+1/2x-5=4x-7/2x+5 equation:

x+1/2x-5=4x-7/2x+5

We move all terms to the left:

x+1/2x-5-(4x-7/2x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

x+1/2x-4x+7/2x-5-5=0

We multiply all the terms by the denominator


x*2x-4x*2x-5*2x-5*2x+1+7=0

We add all the numbers together, and all the variables

x*2x-4x*2x-5*2x-5*2x+8=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2-20x+8=0

a = -6; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·(-6)·8
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{37}}{2*-6}=\frac{20-4\sqrt{37}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{37}}{2*-6}=\frac{20+4\sqrt{37}}{-12}
$