Y=4x2+3x

Solution for Y=4x2+3x equation:

=4Y^2+3Y

We move all terms to the left:

-(4Y^2+3Y)=0

We get rid of parentheses

-4Y^2-3Y=0

a = -4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-4}=\frac{0}{-8}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-4}=\frac{6}{-8}
=-3/4
$