X(3x-11)=4

Solution for X(3x-11)=4 equation:

X(3X-11)=4

We move all terms to the left:

X(3X-11)-(4)=0

We multiply parentheses

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
$