7x(9+x)=238

Solution for 7x(9+x)=238 equation:

7x(9+x)=238

We move all terms to the left:

7x(9+x)-(238)=0

We add all the numbers together, and all the variables

7x(x+9)-238=0

We multiply parentheses

7x^2+63x-238=0

a = 7; b = 63; c = -238;
Δ = b2-4ac
Δ = 632-4·7·(-238)
Δ = 10633
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:

$\sqrt{\Delta}=\sqrt{10633}=\sqrt{49*217}=\sqrt{49}*\sqrt{217}=7\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-7\sqrt{217}}{2*7}=\frac{-63-7\sqrt{217}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+7\sqrt{217}}{2*7}=\frac{-63+7\sqrt{217}}{14}
$