8x^2=17^2

Solution for 8x^2=17^2 equation:

8x^2=17^2

We move all terms to the left:

8x^2-(17^2)=0

We add all the numbers together, and all the variables

8x^2-289=0

a = 8; b = 0; c = -289;
Δ = b2-4ac
Δ = 02-4·8·(-289)
Δ = 9248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9248}=\sqrt{4624*2}=\sqrt{4624}*\sqrt{2}=68\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-68\sqrt{2}}{2*8}=\frac{0-68\sqrt{2}}{16}
=-\frac{68\sqrt{2}}{16}
=-\frac{17\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+68\sqrt{2}}{2*8}=\frac{0+68\sqrt{2}}{16}
=\frac{68\sqrt{2}}{16}
=\frac{17\sqrt{2}}{4}
$