2x(7+x)=34

Solution for 2x(7+x)=34 equation:

2x(7+x)=34

We move all terms to the left:

2x(7+x)-(34)=0

We add all the numbers together, and all the variables

2x(x+7)-34=0

We multiply parentheses

2x^2+14x-34=0

a = 2; b = 14; c = -34;
Δ = b2-4ac
Δ = 142-4·2·(-34)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{13}}{2*2}=\frac{-14-6\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{13}}{2*2}=\frac{-14+6\sqrt{13}}{4}
$