4x+11=3x(x-1)

Solution for 4x+11=3x(x-1) equation:

4x+11=3x(x-1)

We move all terms to the left:

4x+11-(3x(x-1))=0


We calculate terms in parentheses: -(3x(x-1)), so:

3x(x-1)

We multiply parentheses

3x^2-3x

Back to the equation:

-(3x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+7x+11=0

a = -3; b = 7; c = +11;
Δ = b2-4ac
Δ = 72-4·(-3)·11
Δ = 181
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{181}}{2*-3}=\frac{-7-\sqrt{181}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{181}}{2*-3}=\frac{-7+\sqrt{181}}{-6}
$