F(x)=5/6x-15

Solution for F(x)=5/6x-15 equation:

(F)=5/6F-15

We move all terms to the left:

(F)-(5/6F-15)=0


Domain of the equation: 6F-15)!=0

F∈R


We get rid of parentheses

F-5/6F+15=0

We multiply all the terms by the denominator


F*6F+15*6F-5=0

Wy multiply elements

6F^2+90F-5=0

a = 6; b = 90; c = -5;
Δ = b2-4ac
Δ = 902-4·6·(-5)
Δ = 8220
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:

$\sqrt{\Delta}=\sqrt{8220}=\sqrt{4*2055}=\sqrt{4}*\sqrt{2055}=2\sqrt{2055}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2055}}{2*6}=\frac{-90-2\sqrt{2055}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2055}}{2*6}=\frac{-90+2\sqrt{2055}}{12}
$