F(x)=4-0.5x/0.75x-15

Solution for F(x)=4-0.5x/0.75x-15 equation:

(F)=4-0.5F/0.75F-15

We move all terms to the left:

(F)-(4-0.5F/0.75F-15)=0


Domain of the equation: 0.75F-15)!=0

F∈R


We add all the numbers together, and all the variables

F-(-0.5F/0.75F-11)=0

We get rid of parentheses

F+0.5F/0.75F+11=0

We multiply all the terms by the denominator


F*0.75F+0.5F+11*0.75F=0

We add all the numbers together, and all the variables

0.5F+F*0.75F+11*0.75F=0

Wy multiply elements

0F^2+0.5F+0F=0

We add all the numbers together, and all the variables

F^2+1.5F=0

a = 1; b = 1.5; c = 0;
Δ = b2-4ac
Δ = 1.52-4·1·0
Δ = 2.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.5)-\sqrt{2.25}}{2*1}=\frac{-1.5-\sqrt{2.25}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{2.25}}{2*1}=\frac{-1.5+\sqrt{2.25}}{2}
$