Y=-3x^2+5x+4

Solution for Y=-3x^2+5x+4 equation:

=-3Y^2+5Y+4

We move all terms to the left:

-(-3Y^2+5Y+4)=0

We get rid of parentheses

3Y^2-5Y-4=0

a = 3; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·3·(-4)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{73}}{2*3}=\frac{5-\sqrt{73}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*3}=\frac{5+\sqrt{73}}{6}
$