Y=5x^2+7x-4

Solution for Y=5x^2+7x-4 equation:

=5Y^2+7Y-4

We move all terms to the left:

-(5Y^2+7Y-4)=0

We get rid of parentheses

-5Y^2-7Y+4=0

a = -5; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-5)·4
Δ = 129
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{-(-7)-\sqrt{129}}{2*-5}=\frac{7-\sqrt{129}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*-5}=\frac{7+\sqrt{129}}{-10}
$