X(x+6)/2=80

Solution for X(x+6)/2=80 equation:

X(X+6)/2=80

We move all terms to the left:

X(X+6)/2-(80)=0

We multiply all the terms by the denominator


X(X+6)-80*2=0

We add all the numbers together, and all the variables

X(X+6)-160=0

We multiply parentheses

X^2+6X-160=0

a = 1; b = 6; c = -160;
Δ = b2-4ac
Δ = 62-4·1·(-160)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*1}=\frac{20}{2}
=10
$