X=0.1162-2.38(1+x)/48.2

Solution for X=0.1162-2.38(1+x)/48.2 equation:

X=0.1162-2.38(1+X)/48.2

We move all terms to the left:

X-(0.1162-2.38(1+X)/48.2)=0

We add all the numbers together, and all the variables

X-(0.1162-2.38(X+1)/48.2)=0

We multiply all the terms by the denominator


X*48.2)-(0.1162-2.38(X+1)=0

We multiply parentheses

X*48.2)-(0.1162-2.38X-2.38=0

Wy multiply elements

48X^2-2.38X-2.38=0

a = 48; b = -2.38; c = -2.38;
Δ = b2-4ac
Δ = -2.382-4·48·(-2.38)
Δ = 462.6244
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{-(-2.38)-\sqrt{462.6244}}{2*48}=\frac{2.38-\sqrt{462.6244}}{96}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.38)+\sqrt{462.6244}}{2*48}=\frac{2.38+\sqrt{462.6244}}{96}
$