5y^2-24y=200

Solution for 5y^2-24y=200 equation:

5y^2-24y=200

We move all terms to the left:

5y^2-24y-(200)=0

a = 5; b = -24; c = -200;
Δ = b2-4ac
Δ = -242-4·5·(-200)
Δ = 4576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{286}}{2*5}=\frac{24-4\sqrt{286}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{286}}{2*5}=\frac{24+4\sqrt{286}}{10}
$