3x+6/7x+6=0

Solution for 3x+6/7x+6=0 equation:

3x+6/7x+6=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

21x^2+42x+6=0

a = 21; b = 42; c = +6;
Δ = b2-4ac
Δ = 422-4·21·6
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{35}}{2*21}=\frac{-42-6\sqrt{35}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{35}}{2*21}=\frac{-42+6\sqrt{35}}{42}
$