100x2=75

Solution for 100x2=75 equation:

100x^2=75

We move all terms to the left:

100x^2-(75)=0

a = 100; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·100·(-75)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{3}}{2*100}=\frac{0-100\sqrt{3}}{200}
=-\frac{100\sqrt{3}}{200}
=-\frac{\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{3}}{2*100}=\frac{0+100\sqrt{3}}{200}
=\frac{100\sqrt{3}}{200}
=\frac{\sqrt{3}}{2}
$