F(x)=3/5x-18

Solution for F(x)=3/5x-18 equation:

(F)=3/5F-18

We move all terms to the left:

(F)-(3/5F-18)=0


Domain of the equation: 5F-18)!=0

F∈R


We get rid of parentheses

F-3/5F+18=0

We multiply all the terms by the denominator


F*5F+18*5F-3=0

Wy multiply elements

5F^2+90F-3=0

a = 5; b = 90; c = -3;
Δ = b2-4ac
Δ = 902-4·5·(-3)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-4\sqrt{510}}{2*5}=\frac{-90-4\sqrt{510}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+4\sqrt{510}}{2*5}=\frac{-90+4\sqrt{510}}{10}
$