x+5x2-6/2=8

Solution for x+5x2-6/2=8 equation:

x+5x^2-6/2=8

We move all terms to the left:

x+5x^2-6/2-(8)=0

determiningTheFunctionDomain
5x^2+x-8-6/2=0

We add all the numbers together, and all the variables

5x^2+x-11=0

a = 5; b = 1; c = -11;
Δ = b2-4ac
Δ = 12-4·5·(-11)
Δ = 221
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{221}}{2*5}=\frac{-1-\sqrt{221}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{221}}{2*5}=\frac{-1+\sqrt{221}}{10}
$