50=4y^2+10y

Solution for 50=4y^2+10y equation:

50=4y^2+10y

We move all terms to the left:

50-(4y^2+10y)=0

We get rid of parentheses

-4y^2-10y+50=0

a = -4; b = -10; c = +50;
Δ = b2-4ac
Δ = -102-4·(-4)·50
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*-4}=\frac{40}{-8}
=-5
$