1/2x+7x=180

Solution for 1/2x+7x=180 equation:

1/2x+7x=180

We move all terms to the left:

1/2x+7x-(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

7x+1/2x-180=0

We multiply all the terms by the denominator


7x*2x-180*2x+1=0

Wy multiply elements

14x^2-360x+1=0

a = 14; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·14·1
Δ = 129544
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:

$\sqrt{\Delta}=\sqrt{129544}=\sqrt{4*32386}=\sqrt{4}*\sqrt{32386}=2\sqrt{32386}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32386}}{2*14}=\frac{360-2\sqrt{32386}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32386}}{2*14}=\frac{360+2\sqrt{32386}}{28}
$