F(x)=4x+3/5x-3

Solution for F(x)=4x+3/5x-3 equation:

(F)=4F+3/5F-3

We move all terms to the left:

(F)-(4F+3/5F-3)=0


Domain of the equation: 5F-3)!=0

F∈R


We get rid of parentheses

F-4F-3/5F+3=0

We multiply all the terms by the denominator


F*5F-4F*5F+3*5F-3=0

Wy multiply elements

5F^2-20F^2+15F-3=0

We add all the numbers together, and all the variables

-15F^2+15F-3=0

a = -15; b = 15; c = -3;
Δ = b2-4ac
Δ = 152-4·(-15)·(-3)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{5}}{2*-15}=\frac{-15-3\sqrt{5}}{-30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{5}}{2*-15}=\frac{-15+3\sqrt{5}}{-30}
$