2x+3x(3/4x)=23

Solution for 2x+3x(3/4x)=23 equation:

2x+3x(3/4x)=23

We move all terms to the left:

2x+3x(3/4x)-(23)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3x(+3/4x)-23=0

We multiply parentheses

9x^2+2x-23=0

a = 9; b = 2; c = -23;
Δ = b2-4ac
Δ = 22-4·9·(-23)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{13}}{2*9}=\frac{-2-8\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{13}}{2*9}=\frac{-2+8\sqrt{13}}{18}
$