4(2y2)-17=15

Solution for 4(2y2)-17=15 equation:

4(2y^2)-17=15

We move all terms to the left:

4(2y^2)-17-(15)=0

We add all the numbers together, and all the variables

42y^2-32=0

a = 42; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·42·(-32)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*42}=\frac{0-16\sqrt{21}}{84}
=-\frac{16\sqrt{21}}{84}
=-\frac{4\sqrt{21}}{21}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*42}=\frac{0+16\sqrt{21}}{84}
=\frac{16\sqrt{21}}{84}
=\frac{4\sqrt{21}}{21}
$