F(x)=4x-7/5x+6

Solution for F(x)=4x-7/5x+6 equation:

(F)=4F-7/5F+6

We move all terms to the left:

(F)-(4F-7/5F+6)=0


Domain of the equation: 5F+6)!=0

F∈R


We get rid of parentheses

F-4F+7/5F-6=0

We multiply all the terms by the denominator


F*5F-4F*5F-6*5F+7=0

Wy multiply elements

5F^2-20F^2-30F+7=0

We add all the numbers together, and all the variables

-15F^2-30F+7=0

a = -15; b = -30; c = +7;
Δ = b2-4ac
Δ = -302-4·(-15)·7
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{330}}{2*-15}=\frac{30-2\sqrt{330}}{-30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{330}}{2*-15}=\frac{30+2\sqrt{330}}{-30}
$