10x2=12

Solution for 10x2=12 equation:

10x^2=12

We move all terms to the left:

10x^2-(12)=0

a = 10; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·10·(-12)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*10}=\frac{0-4\sqrt{30}}{20}
=-\frac{4\sqrt{30}}{20}
=-\frac{\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*10}=\frac{0+4\sqrt{30}}{20}
=\frac{4\sqrt{30}}{20}
=\frac{\sqrt{30}}{5}
$