11x^2-10x+4=6x^2

Solution for 11x^2-10x+4=6x^2 equation:

11x^2-10x+4=6x^2

We move all terms to the left:

11x^2-10x+4-(6x^2)=0

determiningTheFunctionDomain
11x^2-6x^2-10x+4=0

We add all the numbers together, and all the variables

5x^2-10x+4=0

a = 5; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·5·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*5}=\frac{10-2\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*5}=\frac{10+2\sqrt{5}}{10}
$