4x-2/3x+14=180

Solution for 4x-2/3x+14=180 equation:

4x-2/3x+14=180

We move all terms to the left:

4x-2/3x+14-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-2/3x-166=0

We multiply all the terms by the denominator


4x*3x-166*3x-2=0

Wy multiply elements

12x^2-498x-2=0

a = 12; b = -498; c = -2;
Δ = b2-4ac
Δ = -4982-4·12·(-2)
Δ = 248100
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:

$\sqrt{\Delta}=\sqrt{248100}=\sqrt{100*2481}=\sqrt{100}*\sqrt{2481}=10\sqrt{2481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-498)-10\sqrt{2481}}{2*12}=\frac{498-10\sqrt{2481}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-498)+10\sqrt{2481}}{2*12}=\frac{498+10\sqrt{2481}}{24}
$