1/2x-6=-2x+9

Solution for 1/2x-6=-2x+9 equation:

1/2x-6=-2x+9

We move all terms to the left:

1/2x-6-(-2x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+2x-9-6=0

We multiply all the terms by the denominator


2x*2x-9*2x-6*2x+1=0

Wy multiply elements

4x^2-18x-12x+1=0

We add all the numbers together, and all the variables

4x^2-30x+1=0

a = 4; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·4·1
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{221}}{2*4}=\frac{30-2\sqrt{221}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{221}}{2*4}=\frac{30+2\sqrt{221}}{8}
$