Y=4x2+3x-10

Solution for Y=4x2+3x-10 equation:

=4Y^2+3Y-10

We move all terms to the left:

-(4Y^2+3Y-10)=0

We get rid of parentheses

-4Y^2-3Y+10=0

a = -4; b = -3; c = +10;
Δ = b2-4ac
Δ = -32-4·(-4)·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-4}=\frac{16}{-8}
=-2
$