F(x)=2x+7/3x-5

Solution for F(x)=2x+7/3x-5 equation:

(F)=2F+7/3F-5

We move all terms to the left:

(F)-(2F+7/3F-5)=0


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

F∈R


We get rid of parentheses

F-2F-7/3F+5=0

We multiply all the terms by the denominator


F*3F-2F*3F+5*3F-7=0

Wy multiply elements

3F^2-6F^2+15F-7=0

We add all the numbers together, and all the variables

-3F^2+15F-7=0

a = -3; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·(-3)·(-7)
Δ = 141
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{-(15)-\sqrt{141}}{2*-3}=\frac{-15-\sqrt{141}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{141}}{2*-3}=\frac{-15+\sqrt{141}}{-6}
$