5y2-17y=-6

Solution for 5y2-17y=-6 equation:

5y^2-17y=-6

We move all terms to the left:

5y^2-17y-(-6)=0

We add all the numbers together, and all the variables

5y^2-17y+6=0

a = 5; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·5·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*5}=\frac{4}{10}
=2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*5}=\frac{30}{10}
=3
$