75x^2-5-10=0

Solution for 75x^2-5-10=0 equation:

75x^2-5-10=0

We add all the numbers together, and all the variables

75x^2-15=0

a = 75; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·75·(-15)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*75}=\frac{0-30\sqrt{5}}{150}
=-\frac{30\sqrt{5}}{150}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*75}=\frac{0+30\sqrt{5}}{150}
=\frac{30\sqrt{5}}{150}
=\frac{\sqrt{5}}{5}
$