x^2=-4x+17

Solution for x^2=-4x+17 equation:

x^2=-4x+17

We move all terms to the left:

x^2-(-4x+17)=0

We get rid of parentheses

x^2+4x-17=0

a = 1; b = 4; c = -17;
Δ = b2-4ac
Δ = 42-4·1·(-17)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{21}}{2*1}=\frac{-4-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{21}}{2*1}=\frac{-4+2\sqrt{21}}{2}
$