6x^2-5=-x

Solution for 6x^2-5=-x equation:

6x^2-5=-x

We move all terms to the left:

6x^2-5-(-x)=0

We add all the numbers together, and all the variables

6x^2-(-1x)-5=0

We get rid of parentheses

6x^2+1x-5=0

We add all the numbers together, and all the variables

6x^2+x-5=0

a = 6; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·6·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*6}=\frac{10}{12}
=5/6
$