F(x)=4/3x-5

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

(F)=4/3F-5

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-4/3F+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

3F^2+15F-4=0

a = 3; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·3·(-4)
Δ = 273
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{273}}{2*3}=\frac{-15-\sqrt{273}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*3}=\frac{-15+\sqrt{273}}{6}
$