7+2x=2(2x+6)-(x2)

Solution for 7+2x=2(2x+6)-(x2) equation:

7+2x=2(2x+6)-(x2)

We move all terms to the left:

7+2x-(2(2x+6)-(x2))=0


We calculate terms in parentheses: -(2(2x+6)-x2), so:

2(2x+6)-x2

We add all the numbers together, and all the variables

-1x^2+2(2x+6)

We multiply parentheses

-1x^2+4x+12

Back to the equation:

-(-1x^2+4x+12)


We get rid of parentheses

1x^2-4x+2x-12+7=0

We add all the numbers together, and all the variables

x^2-2x-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$