3x+10+1/2x-5=180

Solution for 3x+10+1/2x-5=180 equation:

3x+10+1/2x-5=180

We move all terms to the left:

3x+10+1/2x-5-(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-175=0

We multiply all the terms by the denominator


3x*2x-175*2x+1=0

Wy multiply elements

6x^2-350x+1=0

a = 6; b = -350; c = +1;
Δ = b2-4ac
Δ = -3502-4·6·1
Δ = 122476
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:

$\sqrt{\Delta}=\sqrt{122476}=\sqrt{4*30619}=\sqrt{4}*\sqrt{30619}=2\sqrt{30619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30619}}{2*6}=\frac{350-2\sqrt{30619}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30619}}{2*6}=\frac{350+2\sqrt{30619}}{12}
$