5x^2-9=51

Solution for 5x^2-9=51 equation:

5x^2-9=51

We move all terms to the left:

5x^2-9-(51)=0

We add all the numbers together, and all the variables

5x^2-60=0

a = 5; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·5·(-60)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*5}=\frac{0-20\sqrt{3}}{10}
=-\frac{20\sqrt{3}}{10}
=-2\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*5}=\frac{0+20\sqrt{3}}{10}
=\frac{20\sqrt{3}}{10}
=2\sqrt{3}
$