8y(2)=144

Solution for 8y(2)=144 equation:

8y(2)=144

We move all terms to the left:

8y(2)-(144)=0

We add all the numbers together, and all the variables

8y^2-144=0

a = 8; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·8·(-144)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{2}}{2*8}=\frac{0-48\sqrt{2}}{16}
=-\frac{48\sqrt{2}}{16}
=-3\sqrt{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*8}=\frac{0+48\sqrt{2}}{16}
=\frac{48\sqrt{2}}{16}
=3\sqrt{2}
$