5y^2-34y=7

Solution for 5y^2-34y=7 equation:

5y^2-34y=7

We move all terms to the left:

5y^2-34y-(7)=0

a = 5; b = -34; c = -7;
Δ = b2-4ac
Δ = -342-4·5·(-7)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-36}{2*5}=\frac{-2}{10}
=-1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+36}{2*5}=\frac{70}{10}
=7
$