10x^2-7=13

Solution for 10x^2-7=13 equation:

10x^2-7=13

We move all terms to the left:

10x^2-7-(13)=0

We add all the numbers together, and all the variables

10x^2-20=0

a = 10; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·10·(-20)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*10}=\frac{0-20\sqrt{2}}{20}
=-\frac{20\sqrt{2}}{20}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*10}=\frac{0+20\sqrt{2}}{20}
=\frac{20\sqrt{2}}{20}
=\sqrt{2}
$