(X-50)x1.1=1.05x

Solution for (X-50)x1.1=1.05x equation:

(X-50)X1.1=1.05X

We move all terms to the left:

(X-50)X1.1-(1.05X)=0

We add all the numbers together, and all the variables

(X-50)X1.1-(+1.05X)=0

We multiply parentheses

X^2-50X-(+1.05X)=0

We get rid of parentheses

X^2-50X-1.05X=0

We add all the numbers together, and all the variables

X^2-51.05X=0

a = 1; b = -51.05; c = 0;
Δ = b2-4ac
Δ = -51.052-4·1·0
Δ = 2606.1025
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{-(-51.05)-\sqrt{2606.1025}}{2*1}=\frac{51.05-\sqrt{2606.1025}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51.05)+\sqrt{2606.1025}}{2*1}=\frac{51.05+\sqrt{2606.1025}}{2}
$