-3/2^x+12=2x-3

Solution for -3/2^x+12=2x-3 equation:

-3/2^x+12=2x-3

We move all terms to the left:

-3/2^x+12-(2x-3)=0


Domain of the equation: 2^x!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-3/2^x-2x+3+12=0

We multiply all the terms by the denominator


-2x*2^x+3*2^x+12*2^x-3=0

Wy multiply elements

-4x^2+6x+24x-3=0

We add all the numbers together, and all the variables

-4x^2+30x-3=0

a = -4; b = 30; c = -3;
Δ = b2-4ac
Δ = 302-4·(-4)·(-3)
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{213}}{2*-4}=\frac{-30-2\sqrt{213}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{213}}{2*-4}=\frac{-30+2\sqrt{213}}{-8}
$