X(x+7)/2=22

Solution for X(x+7)/2=22 equation:

X(X+7)/2=22

We move all terms to the left:

X(X+7)/2-(22)=0

We multiply all the terms by the denominator


X(X+7)-22*2=0

We add all the numbers together, and all the variables

X(X+7)-44=0

We multiply parentheses

X^2+7X-44=0

a = 1; b = 7; c = -44;
Δ = b2-4ac
Δ = 72-4·1·(-44)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*1}=\frac{8}{2}
=4
$