x+988/x-78+6x=5*4x

Solution for x+988/x-78+6x=5*4x equation:

x+988/x-78+6x=5*4x

We move all terms to the left:

x+988/x-78+6x-(5*4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+988/x+6x-(+5*4x)-78=0

We add all the numbers together, and all the variables

7x+988/x-(+5*4x)-78=0

We get rid of parentheses

7x+988/x-5*4x-78=0

We multiply all the terms by the denominator


7x*x-(5*4x)*x-78*x+988=0

We add all the numbers together, and all the variables

7x*x-(+5*4x)*x-78*x+988=0

We add all the numbers together, and all the variables

-78x+7x*x-(+5*4x)*x+988=0

We multiply parentheses

-20x^2-78x+7x*x+988=0

Wy multiply elements

-20x^2+7x^2-78x+988=0

We add all the numbers together, and all the variables

-13x^2-78x+988=0

a = -13; b = -78; c = +988;
Δ = b2-4ac
Δ = -782-4·(-13)·988
Δ = 57460
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:

$\sqrt{\Delta}=\sqrt{57460}=\sqrt{676*85}=\sqrt{676}*\sqrt{85}=26\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-26\sqrt{85}}{2*-13}=\frac{78-26\sqrt{85}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+26\sqrt{85}}{2*-13}=\frac{78+26\sqrt{85}}{-26}
$