9x(4-x)=31

Solution for 9x(4-x)=31 equation:

9x(4-x)=31

We move all terms to the left:

9x(4-x)-(31)=0

We add all the numbers together, and all the variables

9x(-1x+4)-31=0

We multiply parentheses

-9x^2+36x-31=0

a = -9; b = 36; c = -31;
Δ = b2-4ac
Δ = 362-4·(-9)·(-31)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{5}}{2*-9}=\frac{-36-6\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{5}}{2*-9}=\frac{-36+6\sqrt{5}}{-18}
$