35=x(x+16)

Solution for 35=x(x+16) equation:

35=x(x+16)

We move all terms to the left:

35-(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+35=0

We add all the numbers together, and all the variables

-1x^2-16x+35=0

a = -1; b = -16; c = +35;
Δ = b2-4ac
Δ = -162-4·(-1)·35
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{11}}{2*-1}=\frac{16-6\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{11}}{2*-1}=\frac{16+6\sqrt{11}}{-2}
$