F(x)=4/5x-16

Solution for F(x)=4/5x-16 equation:

(F)=4/5F-16

We move all terms to the left:

(F)-(4/5F-16)=0


Domain of the equation: 5F-16)!=0

F∈R


We get rid of parentheses

F-4/5F+16=0

We multiply all the terms by the denominator


F*5F+16*5F-4=0

Wy multiply elements

5F^2+80F-4=0

a = 5; b = 80; c = -4;
Δ = b2-4ac
Δ = 802-4·5·(-4)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*5}=\frac{-80-36\sqrt{5}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*5}=\frac{-80+36\sqrt{5}}{10}
$