F(x)=1/4x+10

Solution for F(x)=1/4x+10 equation:

(F)=1/4F+10

We move all terms to the left:

(F)-(1/4F+10)=0


Domain of the equation: 4F+10)!=0

F∈R


We get rid of parentheses

F-1/4F-10=0

We multiply all the terms by the denominator


F*4F-10*4F-1=0

Wy multiply elements

4F^2-40F-1=0

a = 4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·4·(-1)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{101}}{2*4}=\frac{40-4\sqrt{101}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{101}}{2*4}=\frac{40+4\sqrt{101}}{8}
$