3x^2=10^5

Solution for 3x^2=10^5 equation:

3x^2=10^5

We move all terms to the left:

3x^2-(10^5)=0

We add all the numbers together, and all the variables

3x^2-100000=0

a = 3; b = 0; c = -100000;
Δ = b2-4ac
Δ = 02-4·3·(-100000)
Δ = 1200000
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:

$\sqrt{\Delta}=\sqrt{1200000}=\sqrt{40000*30}=\sqrt{40000}*\sqrt{30}=200\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{30}}{2*3}=\frac{0-200\sqrt{30}}{6}
=-\frac{200\sqrt{30}}{6}
=-\frac{100\sqrt{30}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{30}}{2*3}=\frac{0+200\sqrt{30}}{6}
=\frac{200\sqrt{30}}{6}
=\frac{100\sqrt{30}}{3}
$