Y=4x^2+34x

Solution for Y=4x^2+34x equation:

=4Y^2+34Y

We move all terms to the left:

-(4Y^2+34Y)=0

We get rid of parentheses

-4Y^2-34Y=0

a = -4; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·(-4)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*-4}=\frac{0}{-8}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*-4}=\frac{68}{-8}
=-8+1/2
$