y^2+34y+144=0

Solution for y^2+34y+144=0 equation:

y^2+34y+144=0

a = 1; b = 34; c = +144;
Δ = b2-4ac
Δ = 342-4·1·144
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{145}}{2*1}=\frac{-34-2\sqrt{145}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{145}}{2*1}=\frac{-34+2\sqrt{145}}{2}
$