F(x)=-5/2x+10

Solution for F(x)=-5/2x+10 equation:

(F)=-5/2F+10

We move all terms to the left:

(F)-(-5/2F+10)=0


Domain of the equation: 2F+10)!=0

F∈R


We get rid of parentheses

F+5/2F-10=0

We multiply all the terms by the denominator


F*2F-10*2F+5=0

Wy multiply elements

2F^2-20F+5=0

a = 2; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·2·5
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*2}=\frac{20-6\sqrt{10}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*2}=\frac{20+6\sqrt{10}}{4}
$