x(32+x)=14(22+14)

Solution for x(32+x)=14(22+14) equation:

x(32+x)=14(22+14)

We move all terms to the left:

x(32+x)-(14(22+14))=0

We add all the numbers together, and all the variables

x(x+32)-(1436)=0

We add all the numbers together, and all the variables

x(x+32)-1436=0

We multiply parentheses

x^2+32x-1436=0

a = 1; b = 32; c = -1436;
Δ = b2-4ac
Δ = 322-4·1·(-1436)
Δ = 6768
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:

$\sqrt{\Delta}=\sqrt{6768}=\sqrt{144*47}=\sqrt{144}*\sqrt{47}=12\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{47}}{2*1}=\frac{-32-12\sqrt{47}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{47}}{2*1}=\frac{-32+12\sqrt{47}}{2}
$