5x(x-4)=3(x+2)

Solution for 5x(x-4)=3(x+2) equation:

5x(x-4)=3(x+2)

We move all terms to the left:

5x(x-4)-(3(x+2))=0

We multiply parentheses

5x^2-20x-(3(x+2))=0


We calculate terms in parentheses: -(3(x+2)), so:

3(x+2)

We multiply parentheses

3x+6

Back to the equation:

-(3x+6)


We get rid of parentheses

5x^2-20x-3x-6=0

We add all the numbers together, and all the variables

5x^2-23x-6=0

a = 5; b = -23; c = -6;
Δ = b2-4ac
Δ = -232-4·5·(-6)
Δ = 649
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{-(-23)-\sqrt{649}}{2*5}=\frac{23-\sqrt{649}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{649}}{2*5}=\frac{23+\sqrt{649}}{10}
$