(x+7)2x=8

Solution for (x+7)2x=8 equation:

(x+7)2x=8

We move all terms to the left:

(x+7)2x-(8)=0

We multiply parentheses

2x^2+14x-8=0

a = 2; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·2·(-8)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{65}}{2*2}=\frac{-14-2\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{65}}{2*2}=\frac{-14+2\sqrt{65}}{4}
$