F(x)=-5/4x-10

Solution for F(x)=-5/4x-10 equation:

(F)=-5/4F-10

We move all terms to the left:

(F)-(-5/4F-10)=0


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

F∈R


We get rid of parentheses

F+5/4F+10=0

We multiply all the terms by the denominator


F*4F+10*4F+5=0

Wy multiply elements

4F^2+40F+5=0

a = 4; b = 40; c = +5;
Δ = b2-4ac
Δ = 402-4·4·5
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{95}}{2*4}=\frac{-40-4\sqrt{95}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{95}}{2*4}=\frac{-40+4\sqrt{95}}{8}
$