x*2^x-136=0

Solution for x*2^x-136=0 equation:

x*2^x-136=0

Wy multiply elements

2x^2-136=0

a = 2; b = 0; c = -136;
Δ = b2-4ac
Δ = 02-4·2·(-136)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{17}}{2*2}=\frac{0-8\sqrt{17}}{4}
=-\frac{8\sqrt{17}}{4}
=-2\sqrt{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{17}}{2*2}=\frac{0+8\sqrt{17}}{4}
=\frac{8\sqrt{17}}{4}
=2\sqrt{17}
$