-8=3+x/2x2

Solution for -8=3+x/2x2 equation:

-8=3+x/2x^2

We move all terms to the left:

-8-(3+x/2x^2)=0


Domain of the equation: 2x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-x/2x^2-3-8=0

We multiply all the terms by the denominator


-x-3*2x^2-8*2x^2=0

We add all the numbers together, and all the variables

-1x-3*2x^2-8*2x^2=0

Wy multiply elements

-6x^2-16x^2-1x=0

We add all the numbers together, and all the variables

-22x^2-1x=0

a = -22; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-22)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-22}=\frac{0}{-44}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-22}=\frac{2}{-44}
=-1/22
$