5x(x+2)=38+x

Solution for 5x(x+2)=38+x equation:

5x(x+2)=38+x

We move all terms to the left:

5x(x+2)-(38+x)=0

We add all the numbers together, and all the variables

5x(x+2)-(x+38)=0

We multiply parentheses

5x^2+10x-(x+38)=0

We get rid of parentheses

5x^2+10x-x-38=0

We add all the numbers together, and all the variables

5x^2+9x-38=0

a = 5; b = 9; c = -38;
Δ = b2-4ac
Δ = 92-4·5·(-38)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-29}{2*5}=\frac{-38}{10}
=-3+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+29}{2*5}=\frac{20}{10}
=2
$