6x+x^2=1600

Solution for 6x+x^2=1600 equation:

6x+x^2=1600

We move all terms to the left:

6x+x^2-(1600)=0

a = 1; b = 6; c = -1600;
Δ = b2-4ac
Δ = 62-4·1·(-1600)
Δ = 6436
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:

$\sqrt{\Delta}=\sqrt{6436}=\sqrt{4*1609}=\sqrt{4}*\sqrt{1609}=2\sqrt{1609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1609}}{2*1}=\frac{-6-2\sqrt{1609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1609}}{2*1}=\frac{-6+2\sqrt{1609}}{2}
$