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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

8(x+3)

We multiply parentheses

8x+24

Back to the equation:

-(8x+24)


We get rid of parentheses

x^2+5x-8x-24=0

We add all the numbers together, and all the variables

x^2-3x-24=0

a = 1; b = -3; c = -24;
Δ = b2-4ac
Δ = -32-4·1·(-24)
Δ = 105
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{-(-3)-\sqrt{105}}{2*1}=\frac{3-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*1}=\frac{3+\sqrt{105}}{2}
$