4-11x=3x2

Solution for 4-11x=3x2 equation:

4-11x=3x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-3x^2-11x+4=0

a = -3; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·(-3)·4
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*-3}=\frac{-2}{-6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*-3}=\frac{24}{-6}
=-4
$