10x+x^2=9600

Solution for 10x+x^2=9600 equation:

10x+x^2=9600

We move all terms to the left:

10x+x^2-(9600)=0

a = 1; b = 10; c = -9600;
Δ = b2-4ac
Δ = 102-4·1·(-9600)
Δ = 38500
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:

$\sqrt{\Delta}=\sqrt{38500}=\sqrt{100*385}=\sqrt{100}*\sqrt{385}=10\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{385}}{2*1}=\frac{-10-10\sqrt{385}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{385}}{2*1}=\frac{-10+10\sqrt{385}}{2}
$