7x(6+x)=42

Solution for 7x(6+x)=42 equation:

7x(6+x)=42

We move all terms to the left:

7x(6+x)-(42)=0

We add all the numbers together, and all the variables

7x(x+6)-42=0

We multiply parentheses

7x^2+42x-42=0

a = 7; b = 42; c = -42;
Δ = b2-4ac
Δ = 422-4·7·(-42)
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14\sqrt{15}}{2*7}=\frac{-42-14\sqrt{15}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14\sqrt{15}}{2*7}=\frac{-42+14\sqrt{15}}{14}
$