5y^2+16=42y

Solution for 5y^2+16=42y equation:

5y^2+16=42y

We move all terms to the left:

5y^2+16-(42y)=0

a = 5; b = -42; c = +16;
Δ = b2-4ac
Δ = -422-4·5·16
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-38}{2*5}=\frac{4}{10}
=2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+38}{2*5}=\frac{80}{10}
=8
$