5y2=26y+5

Solution for 5y2=26y+5 equation:

5y^2=26y+5

We move all terms to the left:

5y^2-(26y+5)=0

We get rid of parentheses

5y^2-26y-5=0

a = 5; b = -26; c = -5;
Δ = b2-4ac
Δ = -262-4·5·(-5)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{194}}{2*5}=\frac{26-2\sqrt{194}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{194}}{2*5}=\frac{26+2\sqrt{194}}{10}
$