6x2+7x+9=11x^2

Solution for 6x2+7x+9=11x^2 equation:

6x^2+7x+9=11x^2

We move all terms to the left:

6x^2+7x+9-(11x^2)=0

determiningTheFunctionDomain
6x^2-11x^2+7x+9=0

We add all the numbers together, and all the variables

-5x^2+7x+9=0

a = -5; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-5)·9
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{229}}{2*-5}=\frac{-7-\sqrt{229}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{229}}{2*-5}=\frac{-7+\sqrt{229}}{-10}
$