X^2-3=10x

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

X^2-3=10X

We move all terms to the left:

X^2-3-(10X)=0

a = 1; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·1·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{7}}{2*1}=\frac{10-4\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{7}}{2*1}=\frac{10+4\sqrt{7}}{2}
$