15(15)=x(x+16)

Solution for 15(15)=x(x+16) equation:

15(15)=x(x+16)

We move all terms to the left:

15(15)-(x(x+16))=0


We calculate terms in parentheses: -(x(x+16)), so:

x(x+16)

We multiply parentheses

x^2+16x

Back to the equation:

-(x^2+16x)


We get rid of parentheses

-x^2-16x+1515=0

We add all the numbers together, and all the variables

-1x^2-16x+1515=0

a = -1; b = -16; c = +1515;
Δ = b2-4ac
Δ = -162-4·(-1)·1515
Δ = 6316
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:

$\sqrt{\Delta}=\sqrt{6316}=\sqrt{4*1579}=\sqrt{4}*\sqrt{1579}=2\sqrt{1579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{1579}}{2*-1}=\frac{16-2\sqrt{1579}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{1579}}{2*-1}=\frac{16+2\sqrt{1579}}{-2}
$