X(20+1/2)=40+10x

Solution for X(20+1/2)=40+10x equation:

X(20+1/2)=40+10X

We move all terms to the left:

X(20+1/2)-(40+10X)=0

We add all the numbers together, and all the variables

X(1/2+20)-(10X+40)=0

We multiply parentheses

X^2+20X-(10X+40)=0

We get rid of parentheses

X^2+20X-10X-40=0

We add all the numbers together, and all the variables

X^2+10X-40=0

a = 1; b = 10; c = -40;
Δ = b2-4ac
Δ = 102-4·1·(-40)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{65}}{2*1}=\frac{-10-2\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{65}}{2*1}=\frac{-10+2\sqrt{65}}{2}
$