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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-12x-(5(x+1))=0


We calculate terms in parentheses: -(5(x+1)), so:

5(x+1)

We multiply parentheses

5x+5

Back to the equation:

-(5x+5)


We get rid of parentheses

3x^2-12x-5x-5=0

We add all the numbers together, and all the variables

3x^2-17x-5=0

a = 3; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·3·(-5)
Δ = 349
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{-(-17)-\sqrt{349}}{2*3}=\frac{17-\sqrt{349}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{349}}{2*3}=\frac{17+\sqrt{349}}{6}
$