-4x+8=11-1/2x

Solution for -4x+8=11-1/2x equation:

-4x+8=11-1/2x

We move all terms to the left:

-4x+8-(11-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(-1/2x+11)+8=0

We get rid of parentheses

-4x+1/2x-11+8=0

We multiply all the terms by the denominator


-4x*2x-11*2x+8*2x+1=0

Wy multiply elements

-8x^2-22x+16x+1=0

We add all the numbers together, and all the variables

-8x^2-6x+1=0

a = -8; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-8)·1
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*-8}=\frac{6-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*-8}=\frac{6+2\sqrt{17}}{-16}
$