10.x2-5=3

Solution for 10.x2-5=3 equation:

10.x^2-5=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

10.x^2-8=0

a = 10.; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·10.·(-8)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*10.}=\frac{0-8\sqrt{5}}{20}
=-\frac{8\sqrt{5}}{20}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*10.}=\frac{0+8\sqrt{5}}{20}
=\frac{8\sqrt{5}}{20}
=\frac{2\sqrt{5}}{5}
$