X+x(1.1/1.4)=84

Solution for X+x(1.1/1.4)=84 equation:

X+X(1.1/1.4)=84

We move all terms to the left:

X+X(1.1/1.4)-(84)=0

We add all the numbers together, and all the variables

X+X(+1.1/1.4)-84=0

We multiply parentheses

X^2+X-84=0

a = 1; b = 1; c = -84;
Δ = b2-4ac
Δ = 12-4·1·(-84)
Δ = 337
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{337}}{2*1}=\frac{-1-\sqrt{337}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*1}=\frac{-1+\sqrt{337}}{2}
$