F(x)=-5/2x+15

Solution for F(x)=-5/2x+15 equation:

(F)=-5/2F+15

We move all terms to the left:

(F)-(-5/2F+15)=0


Domain of the equation: 2F+15)!=0

F∈R


We get rid of parentheses

F+5/2F-15=0

We multiply all the terms by the denominator


F*2F-15*2F+5=0

Wy multiply elements

2F^2-30F+5=0

a = 2; b = -30; c = +5;
Δ = b2-4ac
Δ = -302-4·2·5
Δ = 860
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:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{215}}{2*2}=\frac{30-2\sqrt{215}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{215}}{2*2}=\frac{30+2\sqrt{215}}{4}
$