x(x+1)=5-2x

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

x(x+1)=5-2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+3x-5=0

a = 1; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·1·(-5)
Δ = 29
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{29}}{2*1}=\frac{-3-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*1}=\frac{-3+\sqrt{29}}{2}
$