10x(x+2)=5(x+8)

Solution for 10x(x+2)=5(x+8) equation:

10x(x+2)=5(x+8)

We move all terms to the left:

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

We multiply parentheses

10x^2+20x-(5(x+8))=0


We calculate terms in parentheses: -(5(x+8)), so:

5(x+8)

We multiply parentheses

5x+40

Back to the equation:

-(5x+40)


We get rid of parentheses

10x^2+20x-5x-40=0

We add all the numbers together, and all the variables

10x^2+15x-40=0

a = 10; b = 15; c = -40;
Δ = b2-4ac
Δ = 152-4·10·(-40)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{73}}{2*10}=\frac{-15-5\sqrt{73}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{73}}{2*10}=\frac{-15+5\sqrt{73}}{20}
$