-2x+3=1/2x-7

Solution for -2x+3=1/2x-7 equation:

-2x+3=1/2x-7

We move all terms to the left:

-2x+3-(1/2x-7)=0


Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

-2x-1/2x+7+3=0

We multiply all the terms by the denominator


-2x*2x+7*2x+3*2x-1=0

Wy multiply elements

-4x^2+14x+6x-1=0

We add all the numbers together, and all the variables

-4x^2+20x-1=0

a = -4; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-4)·(-1)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*-4}=\frac{-20-8\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*-4}=\frac{-20+8\sqrt{6}}{-8}
$