F(x)=-4/5x-12=

Solution for F(x)=-4/5x-12= equation:

(F)=-4/5F-12=

We move all terms to the left:

(F)-(-4/5F-12)=0


Domain of the equation: 5F-12)!=0

F∈R


We get rid of parentheses

F+4/5F+12=0

We multiply all the terms by the denominator


F*5F+12*5F+4=0

Wy multiply elements

5F^2+60F+4=0

a = 5; b = 60; c = +4;
Δ = b2-4ac
Δ = 602-4·5·4
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{55}}{2*5}=\frac{-60-8\sqrt{55}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{55}}{2*5}=\frac{-60+8\sqrt{55}}{10}
$