(7x+6)(6x+4)/(x^2-2)^2=0

Solution for (7x+6)(6x+4)/(x^2-2)^2=0 equation:

(7x+6)(6x+4)/(x^2-2)^2=0


Domain of the equation: (x^2-2)^2!=0

x∈R


We multiply parentheses ..

(+42x^2+28x+36x+24)/(x^2-2)^2=0

We multiply all the terms by the denominator


(+42x^2+28x+36x+24)=0

We get rid of parentheses

42x^2+28x+36x+24=0

We add all the numbers together, and all the variables

42x^2+64x+24=0

a = 42; b = 64; c = +24;
Δ = b2-4ac
Δ = 642-4·42·24
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8}{2*42}=\frac{-72}{84}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8}{2*42}=\frac{-56}{84}
=-2/3
$