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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(x+3)-(5(-1x+8))=0

We multiply parentheses

2x^2+6x-(5(-1x+8))=0


We calculate terms in parentheses: -(5(-1x+8)), so:

5(-1x+8)

We multiply parentheses

-5x+40

Back to the equation:

-(-5x+40)


We get rid of parentheses

2x^2+6x+5x-40=0

We add all the numbers together, and all the variables

2x^2+11x-40=0

a = 2; b = 11; c = -40;
Δ = b2-4ac
Δ = 112-4·2·(-40)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*2}=\frac{10}{4}
=2+1/2
$