5y2+y=10

Solution for 5y2+y=10 equation:

5y^2+y=10

We move all terms to the left:

5y^2+y-(10)=0

a = 5; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·5·(-10)
Δ = 201
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{-(1)-\sqrt{201}}{2*5}=\frac{-1-\sqrt{201}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*5}=\frac{-1+\sqrt{201}}{10}
$