x(6+x)=315

Solution for x(6+x)=315 equation:

x(6+x)=315

We move all terms to the left:

x(6+x)-(315)=0

We add all the numbers together, and all the variables

x(x+6)-315=0

We multiply parentheses

x^2+6x-315=0

a = 1; b = 6; c = -315;
Δ = b2-4ac
Δ = 62-4·1·(-315)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-36}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+36}{2*1}=\frac{30}{2}
=15
$