x(34-x)=225

Solution for x(34-x)=225 equation:

x(34-x)=225

We move all terms to the left:

x(34-x)-(225)=0

We add all the numbers together, and all the variables

x(-1x+34)-225=0

We multiply parentheses

-1x^2+34x-225=0

a = -1; b = 34; c = -225;
Δ = b2-4ac
Δ = 342-4·(-1)·(-225)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-16}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+16}{2*-1}=\frac{-18}{-2}
=+9
$