x=-6x^2+24x-20

Solution for x=-6x^2+24x-20 equation:

x=-6x^2+24x-20

We move all terms to the left:

x-(-6x^2+24x-20)=0

We get rid of parentheses

6x^2-24x+x+20=0

We add all the numbers together, and all the variables

6x^2-23x+20=0

a = 6; b = -23; c = +20;
Δ = b2-4ac
Δ = -232-4·6·20
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*6}=\frac{16}{12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*6}=\frac{30}{12}
=2+1/2
$