Y=10x^2-10x-120

Solution for Y=10x^2-10x-120 equation:

=10Y^2-10Y-120

We move all terms to the left:

-(10Y^2-10Y-120)=0

We get rid of parentheses

-10Y^2+10Y+120=0

a = -10; b = 10; c = +120;
Δ = b2-4ac
Δ = 102-4·(-10)·120
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-70}{2*-10}=\frac{-80}{-20}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+70}{2*-10}=\frac{60}{-20}
=-3
$