X(1/2)+x(1/6)=150+x

Solution for X(1/2)+x(1/6)=150+x equation:

X(1/2)+X(1/6)=150+X

We move all terms to the left:

X(1/2)+X(1/6)-(150+X)=0

We add all the numbers together, and all the variables

X(+1/2)+X(+1/6)-(X+150)=0

We multiply parentheses

X^2+X^2-(X+150)=0

We get rid of parentheses

X^2+X^2-X-150=0

We add all the numbers together, and all the variables

2X^2-1X-150=0

a = 2; b = -1; c = -150;
Δ = b2-4ac
Δ = -12-4·2·(-150)
Δ = 1201
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{-(-1)-\sqrt{1201}}{2*2}=\frac{1-\sqrt{1201}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1201}}{2*2}=\frac{1+\sqrt{1201}}{4}
$