6x+4+3/2x+67=180

Solution for 6x+4+3/2x+67=180 equation:

6x+4+3/2x+67=180

We move all terms to the left:

6x+4+3/2x+67-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6x+3/2x-109=0

We multiply all the terms by the denominator


6x*2x-109*2x+3=0

Wy multiply elements

12x^2-218x+3=0

a = 12; b = -218; c = +3;
Δ = b2-4ac
Δ = -2182-4·12·3
Δ = 47380
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:

$\sqrt{\Delta}=\sqrt{47380}=\sqrt{4*11845}=\sqrt{4}*\sqrt{11845}=2\sqrt{11845}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-2\sqrt{11845}}{2*12}=\frac{218-2\sqrt{11845}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+2\sqrt{11845}}{2*12}=\frac{218+2\sqrt{11845}}{24}
$