14000=54x+10x^2

Solution for 14000=54x+10x^2 equation:

14000=54x+10x^2

We move all terms to the left:

14000-(54x+10x^2)=0

We get rid of parentheses

-10x^2-54x+14000=0

a = -10; b = -54; c = +14000;
Δ = b2-4ac
Δ = -542-4·(-10)·14000
Δ = 562916
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:

$\sqrt{\Delta}=\sqrt{562916}=\sqrt{4*140729}=\sqrt{4}*\sqrt{140729}=2\sqrt{140729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{140729}}{2*-10}=\frac{54-2\sqrt{140729}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{140729}}{2*-10}=\frac{54+2\sqrt{140729}}{-20}
$