Y=2x^2+24x+70

Solution for Y=2x^2+24x+70 equation:

=2Y^2+24Y+70

We move all terms to the left:

-(2Y^2+24Y+70)=0

We get rid of parentheses

-2Y^2-24Y-70=0

a = -2; b = -24; c = -70;
Δ = b2-4ac
Δ = -242-4·(-2)·(-70)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4}{2*-2}=\frac{20}{-4}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4}{2*-2}=\frac{28}{-4}
=-7
$