(82)+(2x-149)+(1/2x+7)=180

Solution for (82)+(2x-149)+(1/2x+7)=180 equation:

(82)+(2x-149)+(1/2x+7)=180

We move all terms to the left:

(82)+(2x-149)+(1/2x+7)-(180)=0


Domain of the equation: 2x+7)!=0

x∈R


We add all the numbers together, and all the variables

(2x-149)+(1/2x+7)-98=0

We get rid of parentheses

2x+1/2x-149+7-98=0

We multiply all the terms by the denominator


2x*2x-149*2x+7*2x-98*2x+1=0

Wy multiply elements

4x^2-298x+14x-196x+1=0

We add all the numbers together, and all the variables

4x^2-480x+1=0

a = 4; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·4·1
Δ = 230384
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:

$\sqrt{\Delta}=\sqrt{230384}=\sqrt{1936*119}=\sqrt{1936}*\sqrt{119}=44\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-44\sqrt{119}}{2*4}=\frac{480-44\sqrt{119}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+44\sqrt{119}}{2*4}=\frac{480+44\sqrt{119}}{8}
$