Y=4x2+x-3

Solution for Y=4x2+x-3 equation:

=4Y^2+Y-3

We move all terms to the left:

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

We get rid of parentheses

-4Y^2-Y+3=0

We add all the numbers together, and all the variables

-4Y^2-1Y+3=0

a = -4; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-4)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-4}=\frac{-6}{-8}
=3/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-4}=\frac{8}{-8}
=-1
$