2x(x+9)=x+22

Solution for 2x(x+9)=x+22 equation:

2x(x+9)=x+22

We move all terms to the left:

2x(x+9)-(x+22)=0

We multiply parentheses

2x^2+18x-(x+22)=0

We get rid of parentheses

2x^2+18x-x-22=0

We add all the numbers together, and all the variables

2x^2+17x-22=0

a = 2; b = 17; c = -22;
Δ = b2-4ac
Δ = 172-4·2·(-22)
Δ = 465
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{-(17)-\sqrt{465}}{2*2}=\frac{-17-\sqrt{465}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{465}}{2*2}=\frac{-17+\sqrt{465}}{4}
$