X^2-4x=78

Solution for X^2-4x=78 equation:

X^2-4X=78

We move all terms to the left:

X^2-4X-(78)=0

a = 1; b = -4; c = -78;
Δ = b2-4ac
Δ = -42-4·1·(-78)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{82}}{2*1}=\frac{4-2\sqrt{82}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{82}}{2*1}=\frac{4+2\sqrt{82}}{2}
$