(x+17)2x=101

Solution for (x+17)2x=101 equation:

(x+17)2x=101

We move all terms to the left:

(x+17)2x-(101)=0

We multiply parentheses

2x^2+34x-101=0

a = 2; b = 34; c = -101;
Δ = b2-4ac
Δ = 342-4·2·(-101)
Δ = 1964
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:

$\sqrt{\Delta}=\sqrt{1964}=\sqrt{4*491}=\sqrt{4}*\sqrt{491}=2\sqrt{491}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{491}}{2*2}=\frac{-34-2\sqrt{491}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{491}}{2*2}=\frac{-34+2\sqrt{491}}{4}
$