(x)=-6x^2+42x-60

Solution for (x)=-6x^2+42x-60 equation:

(x)=-6x^2+42x-60

We move all terms to the left:

(x)-(-6x^2+42x-60)=0

We get rid of parentheses

6x^2-42x+x+60=0

We add all the numbers together, and all the variables

6x^2-41x+60=0

a = 6; b = -41; c = +60;
Δ = b2-4ac
Δ = -412-4·6·60
Δ = 241
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{-(-41)-\sqrt{241}}{2*6}=\frac{41-\sqrt{241}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{241}}{2*6}=\frac{41+\sqrt{241}}{12}
$