-3x+9/7x+6=0

Solution for -3x+9/7x+6=0 equation:

-3x+9/7x+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+9=0

Wy multiply elements

-21x^2+42x+9=0

a = -21; b = 42; c = +9;
Δ = b2-4ac
Δ = 422-4·(-21)·9
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{70}}{2*-21}=\frac{-42-6\sqrt{70}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{70}}{2*-21}=\frac{-42+6\sqrt{70}}{-42}
$