x/5x+3(x+14)=202

Solution for x/5x+3(x+14)=202 equation:

x/5x+3(x+14)=202

We move all terms to the left:

x/5x+3(x+14)-(202)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

x/5x+3x+42-202=0

We multiply all the terms by the denominator


x+3x*5x+42*5x-202*5x=0

Wy multiply elements

15x^2+x+210x-1010x=0

We add all the numbers together, and all the variables

15x^2-799x=0

a = 15; b = -799; c = 0;
Δ = b2-4ac
Δ = -7992-4·15·0
Δ = 638401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{638401}=799$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-799)-799}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-799)+799}{2*15}=\frac{1598}{30}
=53+4/15
$