-(5x+6)=(6/5x+30)+1

Solution for -(5x+6)=(6/5x+30)+1 equation:

-(5x+6)=(6/5x+30)+1

We move all terms to the left:

-(5x+6)-((6/5x+30)+1)=0


Domain of the equation: 5x+30)+1)!=0

x∈R


We get rid of parentheses

-5x-((6/5x+30)+1)-6=0

We multiply all the terms by the denominator


-5x*5x-6*5x+30)+1)-((6+30)+1)=0

We add all the numbers together, and all the variables

-5x*5x-6*5x+30)+1)-(36+1)=0

We add all the numbers together, and all the variables

-5x*5x-6*5x=0

Wy multiply elements

-25x^2-30x=0

a = -25; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-25)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-25}=\frac{0}{-50}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-25}=\frac{60}{-50}
=-1+1/5
$