Y=4x^2+6x-7

Solution for Y=4x^2+6x-7 equation:

=4Y^2+6Y-7

We move all terms to the left:

-(4Y^2+6Y-7)=0

We get rid of parentheses

-4Y^2-6Y+7=0

a = -4; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-4)·7
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{37}}{2*-4}=\frac{6-2\sqrt{37}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{37}}{2*-4}=\frac{6+2\sqrt{37}}{-8}
$