2(3/4)x+31+3x+11=180

Solution for 2(3/4)x+31+3x+11=180 equation:

2(3/4)x+31+3x+11=180

We move all terms to the left:

2(3/4)x+31+3x+11-(180)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(+3/4)x+3x+31+11-180=0

We add all the numbers together, and all the variables

3x+2(+3/4)x-138=0

We multiply parentheses

6x^2+3x-138=0

a = 6; b = 3; c = -138;
Δ = b2-4ac
Δ = 32-4·6·(-138)
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9\sqrt{41}}{2*6}=\frac{-3-9\sqrt{41}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9\sqrt{41}}{2*6}=\frac{-3+9\sqrt{41}}{12}
$