17x^2=51

Solution for 17x^2=51 equation:

17x^2=51

We move all terms to the left:

17x^2-(51)=0

a = 17; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·17·(-51)
Δ = 3468
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:

$\sqrt{\Delta}=\sqrt{3468}=\sqrt{1156*3}=\sqrt{1156}*\sqrt{3}=34\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{3}}{2*17}=\frac{0-34\sqrt{3}}{34}
=-\frac{34\sqrt{3}}{34}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{3}}{2*17}=\frac{0+34\sqrt{3}}{34}
=\frac{34\sqrt{3}}{34}
=\sqrt{3}
$