42y-4y^2=90

Solution for 42y-4y^2=90 equation:

42y-4y^2=90

We move all terms to the left:

42y-4y^2-(90)=0

a = -4; b = 42; c = -90;
Δ = b2-4ac
Δ = 422-4·(-4)·(-90)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-18}{2*-4}=\frac{-60}{-8}
=7+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+18}{2*-4}=\frac{-24}{-8}
=+3
$