1/2x-7x=10

Solution for 1/2x-7x=10 equation:

1/2x-7x=10

We move all terms to the left:

1/2x-7x-(10)=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-10=0

We multiply all the terms by the denominator


-7x*2x-10*2x+1=0

Wy multiply elements

-14x^2-20x+1=0

a = -14; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-14)·1
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{114}}{2*-14}=\frac{20-2\sqrt{114}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{114}}{2*-14}=\frac{20+2\sqrt{114}}{-28}
$