z^2-24z+49=0

Solution for z^2-24z+49=0 equation:

z^2-24z+49=0

a = 1; b = -24; c = +49;
Δ = b2-4ac
Δ = -242-4·1·49
Δ = 380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{95}}{2*1}=\frac{24-2\sqrt{95}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{95}}{2*1}=\frac{24+2\sqrt{95}}{2}
$