F(x)=3/5x-18

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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} $

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