8x^2-30-45=0

Solution for 8x^2-30-45=0 equation:

8x^2-30-45=0

We add all the numbers together, and all the variables

8x^2-75=0

a = 8; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·8·(-75)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*8}=\frac{0-20\sqrt{6}}{16}
=-\frac{20\sqrt{6}}{16}
=-\frac{5\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*8}=\frac{0+20\sqrt{6}}{16}
=\frac{20\sqrt{6}}{16}
=\frac{5\sqrt{6}}{4}
$