-103+24x+x^2=0

Solution for -103+24x+x^2=0 equation:

-103+24x+x^2=0

a = 1; b = 24; c = -103;
Δ = b2-4ac
Δ = 242-4·1·(-103)
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{247}}{2*1}=\frac{-24-2\sqrt{247}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{247}}{2*1}=\frac{-24+2\sqrt{247}}{2}
$