5x(x+2)=3(x+8)

Solution for 5x(x+2)=3(x+8) equation:

5x(x+2)=3(x+8)

We move all terms to the left:

5x(x+2)-(3(x+8))=0

We multiply parentheses

5x^2+10x-(3(x+8))=0


We calculate terms in parentheses: -(3(x+8)), so:

3(x+8)

We multiply parentheses

3x+24

Back to the equation:

-(3x+24)


We get rid of parentheses

5x^2+10x-3x-24=0

We add all the numbers together, and all the variables

5x^2+7x-24=0

a = 5; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·5·(-24)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*5}=\frac{16}{10}
=1+3/5
$