x+(x-45)+(x-35)+1/2x=350

Solution for x+(x-45)+(x-35)+1/2x=350 equation:

x+(x-45)+(x-35)+1/2x=350

We move all terms to the left:

x+(x-45)+(x-35)+1/2x-(350)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x+x+x+1/2x-45-35-350=0

We multiply all the terms by the denominator


x*2x+x*2x+x*2x-45*2x-35*2x-350*2x+1=0

Wy multiply elements

2x^2+2x^2+2x^2-90x-70x-700x+1=0

We add all the numbers together, and all the variables

6x^2-860x+1=0

a = 6; b = -860; c = +1;
Δ = b2-4ac
Δ = -8602-4·6·1
Δ = 739576
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:

$\sqrt{\Delta}=\sqrt{739576}=\sqrt{4*184894}=\sqrt{4}*\sqrt{184894}=2\sqrt{184894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-860)-2\sqrt{184894}}{2*6}=\frac{860-2\sqrt{184894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-860)+2\sqrt{184894}}{2*6}=\frac{860+2\sqrt{184894}}{12}
$