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

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

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

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

X*5)-(-2X-4=0

Wy multiply elements

5X^2-2X-4=0

a = 5; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·5·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*5}=\frac{2-2\sqrt{21}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*5}=\frac{2+2\sqrt{21}}{10}
$