5x(x-2)=2(x+6)

Solution for 5x(x-2)=2(x+6) equation:

5x(x-2)=2(x+6)

We move all terms to the left:

5x(x-2)-(2(x+6))=0

We multiply parentheses

5x^2-10x-(2(x+6))=0


We calculate terms in parentheses: -(2(x+6)), so:

2(x+6)

We multiply parentheses

2x+12

Back to the equation:

-(2x+12)


We get rid of parentheses

5x^2-10x-2x-12=0

We add all the numbers together, and all the variables

5x^2-12x-12=0

a = 5; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·5·(-12)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*5}=\frac{12-8\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*5}=\frac{12+8\sqrt{6}}{10}
$