4^x=3/2x+5

Solution for 4^x=3/2x+5 equation:

4^x=3/2x+5

We move all terms to the left:

4^x-(3/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

4^x-3/2x-5=0

We multiply all the terms by the denominator


4^x*2x-5*2x-3=0

Wy multiply elements

8x^2-10x-3=0

a = 8; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·8·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*8}=\frac{24}{16}
=1+1/2
$