2/5x+7+3/5x=14+x

Solution for 2/5x+7+3/5x=14+x equation:

2/5x+7+3/5x=14+x

We move all terms to the left:

2/5x+7+3/5x-(14+x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x+3/5x-(x+14)+7=0

We get rid of parentheses

2/5x+3/5x-x-14+7=0

We multiply all the terms by the denominator


-x*5x-14*5x+7*5x+2+3=0

We add all the numbers together, and all the variables

-x*5x-14*5x+7*5x+5=0

Wy multiply elements

-5x^2-70x+35x+5=0

We add all the numbers together, and all the variables

-5x^2-35x+5=0

a = -5; b = -35; c = +5;
Δ = b2-4ac
Δ = -352-4·(-5)·5
Δ = 1325
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:

$\sqrt{\Delta}=\sqrt{1325}=\sqrt{25*53}=\sqrt{25}*\sqrt{53}=5\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{53}}{2*-5}=\frac{35-5\sqrt{53}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{53}}{2*-5}=\frac{35+5\sqrt{53}}{-10}
$