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

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

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

We move all terms to the left:

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


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

(x+2)

We get rid of parentheses

x+2

Back to the equation:

-(x+2)


We get rid of parentheses

5x^2-3x-x-2-8=0

We add all the numbers together, and all the variables

5x^2-4x-10=0

a = 5; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·5·(-10)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{6}}{2*5}=\frac{4-6\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{6}}{2*5}=\frac{4+6\sqrt{6}}{10}
$