x/2^x+7=4x-3

Solution for x/2^x+7=4x-3 equation:

x/2^x+7=4x-3

We move all terms to the left:

x/2^x+7-(4x-3)=0


Domain of the equation: 2^x!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x/2^x-4x+3+7=0

We multiply all the terms by the denominator


x-4x*2^x+3*2^x+7*2^x=0

Wy multiply elements

-8x^2+x+6x+14x=0

We add all the numbers together, and all the variables

-8x^2+21x=0

a = -8; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-8)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-8}=\frac{-42}{-16}
=2+5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-8}=\frac{0}{-16}
=0
$