x-40+1/2x-20+3x-70=180

Solution for x-40+1/2x-20+3x-70=180 equation:

x-40+1/2x-20+3x-70=180

We move all terms to the left:

x-40+1/2x-20+3x-70-(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

4x+1/2x-310=0

We multiply all the terms by the denominator


4x*2x-310*2x+1=0

Wy multiply elements

8x^2-620x+1=0

a = 8; b = -620; c = +1;
Δ = b2-4ac
Δ = -6202-4·8·1
Δ = 384368
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:

$\sqrt{\Delta}=\sqrt{384368}=\sqrt{16*24023}=\sqrt{16}*\sqrt{24023}=4\sqrt{24023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-620)-4\sqrt{24023}}{2*8}=\frac{620-4\sqrt{24023}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-620)+4\sqrt{24023}}{2*8}=\frac{620+4\sqrt{24023}}{16}
$