x+9=2x(x+7)

Solution for x+9=2x(x+7) equation:

x+9=2x(x+7)

We move all terms to the left:

x+9-(2x(x+7))=0


We calculate terms in parentheses: -(2x(x+7)), so:

2x(x+7)

We multiply parentheses

2x^2+14x

Back to the equation:

-(2x^2+14x)


We get rid of parentheses

-2x^2+x-14x+9=0

We add all the numbers together, and all the variables

-2x^2-13x+9=0

a = -2; b = -13; c = +9;
Δ = b2-4ac
Δ = -132-4·(-2)·9
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{241}}{2*-2}=\frac{13-\sqrt{241}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{241}}{2*-2}=\frac{13+\sqrt{241}}{-4}
$