F(x)=3/4x+6

Solution for F(x)=3/4x+6 equation:

(F)=3/4F+6

We move all terms to the left:

(F)-(3/4F+6)=0


Domain of the equation: 4F+6)!=0

F∈R


We get rid of parentheses

F-3/4F-6=0

We multiply all the terms by the denominator


F*4F-6*4F-3=0

Wy multiply elements

4F^2-24F-3=0

a = 4; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·4·(-3)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*4}=\frac{24-4\sqrt{39}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*4}=\frac{24+4\sqrt{39}}{8}
$