4x+(1/2x+6)=180

Solution for 4x+(1/2x+6)=180 equation:

4x+(1/2x+6)=180

We move all terms to the left:

4x+(1/2x+6)-(180)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

4x+1/2x+6-180=0

We multiply all the terms by the denominator


4x*2x+6*2x-180*2x+1=0

Wy multiply elements

8x^2+12x-360x+1=0

We add all the numbers together, and all the variables

8x^2-348x+1=0

a = 8; b = -348; c = +1;
Δ = b2-4ac
Δ = -3482-4·8·1
Δ = 121072
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:

$\sqrt{\Delta}=\sqrt{121072}=\sqrt{16*7567}=\sqrt{16}*\sqrt{7567}=4\sqrt{7567}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-4\sqrt{7567}}{2*8}=\frac{348-4\sqrt{7567}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+4\sqrt{7567}}{2*8}=\frac{348+4\sqrt{7567}}{16}
$