1/7x+10=x-50

Solution for 1/7x+10=x-50 equation:

1/7x+10=x-50

We move all terms to the left:

1/7x+10-(x-50)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-x+50+10=0

We multiply all the terms by the denominator


-x*7x+50*7x+10*7x+1=0

Wy multiply elements

-7x^2+350x+70x+1=0

We add all the numbers together, and all the variables

-7x^2+420x+1=0

a = -7; b = 420; c = +1;
Δ = b2-4ac
Δ = 4202-4·(-7)·1
Δ = 176428
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:

$\sqrt{\Delta}=\sqrt{176428}=\sqrt{4*44107}=\sqrt{4}*\sqrt{44107}=2\sqrt{44107}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-2\sqrt{44107}}{2*-7}=\frac{-420-2\sqrt{44107}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+2\sqrt{44107}}{2*-7}=\frac{-420+2\sqrt{44107}}{-14}
$