F(x)=3/4x-18

Solution for F(x)=3/4x-18 equation:

(F)=3/4F-18

We move all terms to the left:

(F)-(3/4F-18)=0


Domain of the equation: 4F-18)!=0

F∈R


We get rid of parentheses

F-3/4F+18=0

We multiply all the terms by the denominator


F*4F+18*4F-3=0

Wy multiply elements

4F^2+72F-3=0

a = 4; b = 72; c = -3;
Δ = b2-4ac
Δ = 722-4·4·(-3)
Δ = 5232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5232}=\sqrt{16*327}=\sqrt{16}*\sqrt{327}=4\sqrt{327}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{327}}{2*4}=\frac{-72-4\sqrt{327}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{327}}{2*4}=\frac{-72+4\sqrt{327}}{8}
$