x(9x+14)=4000

Solution for x(9x+14)=4000 equation:

x(9x+14)=4000

We move all terms to the left:

x(9x+14)-(4000)=0

We multiply parentheses

9x^2+14x-4000=0

a = 9; b = 14; c = -4000;
Δ = b2-4ac
Δ = 142-4·9·(-4000)
Δ = 144196
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:

$\sqrt{\Delta}=\sqrt{144196}=\sqrt{4*36049}=\sqrt{4}*\sqrt{36049}=2\sqrt{36049}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{36049}}{2*9}=\frac{-14-2\sqrt{36049}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{36049}}{2*9}=\frac{-14+2\sqrt{36049}}{18}
$