1/2x+25+3x+15=180

Solution for 1/2x+25+3x+15=180 equation:

1/2x+25+3x+15=180

We move all terms to the left:

1/2x+25+3x+15-(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

3x+1/2x-140=0

We multiply all the terms by the denominator


3x*2x-140*2x+1=0

Wy multiply elements

6x^2-280x+1=0

a = 6; b = -280; c = +1;
Δ = b2-4ac
Δ = -2802-4·6·1
Δ = 78376
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:

$\sqrt{\Delta}=\sqrt{78376}=\sqrt{4*19594}=\sqrt{4}*\sqrt{19594}=2\sqrt{19594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-2\sqrt{19594}}{2*6}=\frac{280-2\sqrt{19594}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+2\sqrt{19594}}{2*6}=\frac{280+2\sqrt{19594}}{12}
$