5x(x+2)=1+x/2

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

5x(x+2)=1+x/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x^2+10x-(x/2+1)=0

We get rid of parentheses

5x^2+10x-x/2-1=0

We multiply all the terms by the denominator


5x^2*2+10x*2-x-1*2=0

We add all the numbers together, and all the variables

5x^2*2-1x+10x*2-2=0

Wy multiply elements

10x^2-1x+20x-2=0

We add all the numbers together, and all the variables

10x^2+19x-2=0

a = 10; b = 19; c = -2;
Δ = b2-4ac
Δ = 192-4·10·(-2)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*10}=\frac{-40}{20}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*10}=\frac{2}{20}
=1/10
$