X^2-6x=53

Solution for X^2-6x=53 equation:

X^2-6X=53

We move all terms to the left:

X^2-6X-(53)=0

a = 1; b = -6; c = -53;
Δ = b2-4ac
Δ = -62-4·1·(-53)
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{62}}{2*1}=\frac{6-2\sqrt{62}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{62}}{2*1}=\frac{6+2\sqrt{62}}{2}
$