Y=5x^2+3x-7

Solution for Y=5x^2+3x-7 equation:

=5Y^2+3Y-7

We move all terms to the left:

-(5Y^2+3Y-7)=0

We get rid of parentheses

-5Y^2-3Y+7=0

a = -5; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-5)·7
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{149}}{2*-5}=\frac{3-\sqrt{149}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{149}}{2*-5}=\frac{3+\sqrt{149}}{-10}
$