F(x)=3/4x-8

Solution for F(x)=3/4x-8 equation:

(F)=3/4F-8

We move all terms to the left:

(F)-(3/4F-8)=0


Domain of the equation: 4F-8)!=0

F∈R


We get rid of parentheses

F-3/4F+8=0

We multiply all the terms by the denominator


F*4F+8*4F-3=0

Wy multiply elements

4F^2+32F-3=0

a = 4; b = 32; c = -3;
Δ = b2-4ac
Δ = 322-4·4·(-3)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{67}}{2*4}=\frac{-32-4\sqrt{67}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{67}}{2*4}=\frac{-32+4\sqrt{67}}{8}
$