5(x-1)=4(3x+12)11x

Solution for 5(x-1)=4(3x+12)11x equation:

5(x-1)=4(3x+12)11x

We move all terms to the left:

5(x-1)-(4(3x+12)11x)=0

We multiply parentheses

5x-(4(3x+12)11x)-5=0


We calculate terms in parentheses: -(4(3x+12)11x), so:

4(3x+12)11x

We multiply parentheses

132x^2+528x

Back to the equation:

-(132x^2+528x)


We get rid of parentheses

-132x^2+5x-528x-5=0

We add all the numbers together, and all the variables

-132x^2-523x-5=0

a = -132; b = -523; c = -5;
Δ = b2-4ac
Δ = -5232-4·(-132)·(-5)
Δ = 270889
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{-(-523)-\sqrt{270889}}{2*-132}=\frac{523-\sqrt{270889}}{-264}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-523)+\sqrt{270889}}{2*-132}=\frac{523+\sqrt{270889}}{-264}
$