7/(x+5)-8(6x+30)=-2

Solution for 7/(x+5)-8(6x+30)=-2 equation:

7/(x+5)-8(6x+30)=-2

We move all terms to the left:

7/(x+5)-8(6x+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(6x+30)+2=0

We multiply parentheses

7/(x+5)-48x-240+2=0

We multiply all the terms by the denominator


-48x*(x+5)-240*(x+5)+2*(x+5)+7=0

We multiply parentheses

-48x^2-240x-240x+2x-1200+10+7=0

We add all the numbers together, and all the variables

-48x^2-478x-1183=0

a = -48; b = -478; c = -1183;
Δ = b2-4ac
Δ = -4782-4·(-48)·(-1183)
Δ = 1348
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:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-478)-2\sqrt{337}}{2*-48}=\frac{478-2\sqrt{337}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-478)+2\sqrt{337}}{2*-48}=\frac{478+2\sqrt{337}}{-96}
$