8/7x+5x=3x+19+9

Solution for 8/7x+5x=3x+19+9 equation:

8/7x+5x=3x+19+9

We move all terms to the left:

8/7x+5x-(3x+19+9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

8/7x+5x-(3x+28)=0

We add all the numbers together, and all the variables

5x+8/7x-(3x+28)=0

We get rid of parentheses

5x+8/7x-3x-28=0

We multiply all the terms by the denominator


5x*7x-3x*7x-28*7x+8=0

Wy multiply elements

35x^2-21x^2-196x+8=0

We add all the numbers together, and all the variables

14x^2-196x+8=0

a = 14; b = -196; c = +8;
Δ = b2-4ac
Δ = -1962-4·14·8
Δ = 37968
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:

$\sqrt{\Delta}=\sqrt{37968}=\sqrt{16*2373}=\sqrt{16}*\sqrt{2373}=4\sqrt{2373}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-4\sqrt{2373}}{2*14}=\frac{196-4\sqrt{2373}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+4\sqrt{2373}}{2*14}=\frac{196+4\sqrt{2373}}{28}
$