7/(x+5)-8(66x+30)=-2

Solution for 7/(x+5)-8(66x+30)=-2 equation:

7/(x+5)-8(66x+30)=-2

We move all terms to the left:

7/(x+5)-8(66x+30)-(-2)=0


Domain of the equation: (x+5)!=0

We move all terms containing x to the left, all other terms to the right

x!=-5

x∈R


We add all the numbers together, and all the variables

7/(x+5)-8(66x+30)+2=0

We multiply parentheses

7/(x+5)-528x-240+2=0

We multiply all the terms by the denominator


-528x*(x+5)-240*(x+5)+2*(x+5)+7=0

We multiply parentheses

-528x^2-2640x-240x+2x-1200+10+7=0

We add all the numbers together, and all the variables

-528x^2-2878x-1183=0

a = -528; b = -2878; c = -1183;
Δ = b2-4ac
Δ = -28782-4·(-528)·(-1183)
Δ = 5784388
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:

$\sqrt{\Delta}=\sqrt{5784388}=\sqrt{4*1446097}=\sqrt{4}*\sqrt{1446097}=2\sqrt{1446097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2878)-2\sqrt{1446097}}{2*-528}=\frac{2878-2\sqrt{1446097}}{-1056}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2878)+2\sqrt{1446097}}{2*-528}=\frac{2878+2\sqrt{1446097}}{-1056}
$