6x+7/3x+5=-5

Solution for 6x+7/3x+5=-5 equation:

6x+7/3x+5=-5

We move all terms to the left:

6x+7/3x+5-(-5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

6x+7/3x+10=0

We multiply all the terms by the denominator


6x*3x+10*3x+7=0

Wy multiply elements

18x^2+30x+7=0

a = 18; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·18·7
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{11}}{2*18}=\frac{-30-6\sqrt{11}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{11}}{2*18}=\frac{-30+6\sqrt{11}}{36}
$