5y^2-42y-234=0

Solution for 5y^2-42y-234=0 equation:

5y^2-42y-234=0

a = 5; b = -42; c = -234;
Δ = b2-4ac
Δ = -422-4·5·(-234)
Δ = 6444
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:

$\sqrt{\Delta}=\sqrt{6444}=\sqrt{36*179}=\sqrt{36}*\sqrt{179}=6\sqrt{179}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{179}}{2*5}=\frac{42-6\sqrt{179}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{179}}{2*5}=\frac{42+6\sqrt{179}}{10}
$