10x+x^2=1120

Solution for 10x+x^2=1120 equation:

10x+x^2=1120

We move all terms to the left:

10x+x^2-(1120)=0

a = 1; b = 10; c = -1120;
Δ = b2-4ac
Δ = 102-4·1·(-1120)
Δ = 4580
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:

$\sqrt{\Delta}=\sqrt{4580}=\sqrt{4*1145}=\sqrt{4}*\sqrt{1145}=2\sqrt{1145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1145}}{2*1}=\frac{-10-2\sqrt{1145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1145}}{2*1}=\frac{-10+2\sqrt{1145}}{2}
$