x^2-3=6x-10

Solution for x^2-3=6x-10 equation:

x^2-3=6x-10

We move all terms to the left:

x^2-3-(6x-10)=0

We get rid of parentheses

x^2-6x+10-3=0

We add all the numbers together, and all the variables

x^2-6x+7=0

a = 1; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·1·7
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{2}}{2*1}=\frac{6-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{2}}{2*1}=\frac{6+2\sqrt{2}}{2}
$