x=-6x^2+5x+10

Solution for x=-6x^2+5x+10 equation:

x=-6x^2+5x+10

We move all terms to the left:

x-(-6x^2+5x+10)=0

We get rid of parentheses

6x^2-5x+x-10=0

We add all the numbers together, and all the variables

6x^2-4x-10=0

a = 6; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·6·(-10)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*6}=\frac{20}{12}
=1+2/3
$