F(-3)=8x-5/9x+4

Solution for F(-3)=8x-5/9x+4 equation:

(-3)=8F-5/9F+4

We move all terms to the left:

(-3)-(8F-5/9F+4)=0


Domain of the equation: 9F+4)!=0

F∈R


We add all the numbers together, and all the variables

-(8F-5/9F+4)-3=0

We get rid of parentheses

-8F+5/9F-4-3=0

We multiply all the terms by the denominator


-8F*9F-4*9F-3*9F+5=0

Wy multiply elements

-72F^2-36F-27F+5=0

We add all the numbers together, and all the variables

-72F^2-63F+5=0

a = -72; b = -63; c = +5;
Δ = b2-4ac
Δ = -632-4·(-72)·5
Δ = 5409
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:

$\sqrt{\Delta}=\sqrt{5409}=\sqrt{9*601}=\sqrt{9}*\sqrt{601}=3\sqrt{601}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{601}}{2*-72}=\frac{63-3\sqrt{601}}{-144}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{601}}{2*-72}=\frac{63+3\sqrt{601}}{-144}
$