(X+2)2+(2x-1)2=5x(x+1)

Solution for (X+2)2+(2x-1)2=5x(x+1) equation:

(X+2)2+(2X-1)2=5X(X+1)

We move all terms to the left:

(X+2)2+(2X-1)2-(5X(X+1))=0

We multiply parentheses

2X+4X-(5X(X+1))+4-2=0


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

5X(X+1)

We multiply parentheses

5X^2+5X

Back to the equation:

-(5X^2+5X)


We add all the numbers together, and all the variables

6X-(5X^2+5X)+2=0

We get rid of parentheses

-5X^2+6X-5X+2=0

We add all the numbers together, and all the variables

-5X^2+X+2=0

a = -5; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-5)·2
Δ = 41
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{-(1)-\sqrt{41}}{2*-5}=\frac{-1-\sqrt{41}}{-10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-5}=\frac{-1+\sqrt{41}}{-10}
$