x/7x+10=4x+40

Solution for x/7x+10=4x+40 equation:

x/7x+10=4x+40

We move all terms to the left:

x/7x+10-(4x+40)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

x/7x-4x-40+10=0

We multiply all the terms by the denominator


x-4x*7x-40*7x+10*7x=0

Wy multiply elements

-28x^2+x-280x+70x=0

We add all the numbers together, and all the variables

-28x^2-209x=0

a = -28; b = -209; c = 0;
Δ = b2-4ac
Δ = -2092-4·(-28)·0
Δ = 43681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43681}=209$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-209)-209}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-209)+209}{2*-28}=\frac{418}{-56}
=-7+13/28
$