45x^2-48=0

Solution for 45x^2-48=0 equation:

45x^2-48=0

a = 45; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·45·(-48)
Δ = 8640
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:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{15}}{2*45}=\frac{0-24\sqrt{15}}{90}
=-\frac{24\sqrt{15}}{90}
=-\frac{4\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{15}}{2*45}=\frac{0+24\sqrt{15}}{90}
=\frac{24\sqrt{15}}{90}
=\frac{4\sqrt{15}}{15}
$