F(x)=32/5x-20

Solution for F(x)=32/5x-20 equation:

(F)=32/5F-20

We move all terms to the left:

(F)-(32/5F-20)=0


Domain of the equation: 5F-20)!=0

F∈R


We get rid of parentheses

F-32/5F+20=0

We multiply all the terms by the denominator


F*5F+20*5F-32=0

Wy multiply elements

5F^2+100F-32=0

a = 5; b = 100; c = -32;
Δ = b2-4ac
Δ = 1002-4·5·(-32)
Δ = 10640
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:

$\sqrt{\Delta}=\sqrt{10640}=\sqrt{16*665}=\sqrt{16}*\sqrt{665}=4\sqrt{665}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{665}}{2*5}=\frac{-100-4\sqrt{665}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{665}}{2*5}=\frac{-100+4\sqrt{665}}{10}
$