Y=5x^2-10x-7

Solution for Y=5x^2-10x-7 equation:

=5Y^2-10Y-7

We move all terms to the left:

-(5Y^2-10Y-7)=0

We get rid of parentheses

-5Y^2+10Y+7=0

a = -5; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-5)·7
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{15}}{2*-5}=\frac{-10-4\sqrt{15}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{15}}{2*-5}=\frac{-10+4\sqrt{15}}{-10}
$