4x^2-3/11=x

Solution for 4x^2-3/11=x equation:

4x^2-3/11=x

We move all terms to the left:

4x^2-3/11-(x)=0

We add all the numbers together, and all the variables

4x^2-1x-3/11=0

We multiply all the terms by the denominator


4x^2*11-1x*11-3=0

Wy multiply elements

44x^2-11x-3=0

a = 44; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·44·(-3)
Δ = 649
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{-(-11)-\sqrt{649}}{2*44}=\frac{11-\sqrt{649}}{88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{649}}{2*44}=\frac{11+\sqrt{649}}{88}
$