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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+14x+10x-1=0

We add all the numbers together, and all the variables

-4x^2+24x-1=0

a = -4; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-4)·(-1)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{35}}{2*-4}=\frac{-24-4\sqrt{35}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{35}}{2*-4}=\frac{-24+4\sqrt{35}}{-8}
$