1/2x-7=2x-5

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



1/2x-7=2x-5
We move all terms to the left:
1/2x-7-(2x-5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
1/2x-2x+5-7=0
We multiply all the terms by the denominator
-2x*2x+5*2x-7*2x+1=0
Wy multiply elements
-4x^2+10x-14x+1=0
We add all the numbers together, and all the variables
-4x^2-4x+1=0
a = -4; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-4)·1
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{-(-4)-4\sqrt{2}}{2*-4}=\frac{4-4\sqrt{2}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-4}=\frac{4+4\sqrt{2}}{-8} $

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