Y=4x^2+7x-36

Solution for Y=4x^2+7x-36 equation:

=4Y^2+7Y-36

We move all terms to the left:

-(4Y^2+7Y-36)=0

We get rid of parentheses

-4Y^2-7Y+36=0

a = -4; b = -7; c = +36;
Δ = b2-4ac
Δ = -72-4·(-4)·36
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*-4}=\frac{32}{-8}
=-4
$