F(x)=2/5x-12

Solution for F(x)=2/5x-12 equation:

(F)=2/5F-12

We move all terms to the left:

(F)-(2/5F-12)=0


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

F∈R


We get rid of parentheses

F-2/5F+12=0

We multiply all the terms by the denominator


F*5F+12*5F-2=0

Wy multiply elements

5F^2+60F-2=0

a = 5; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·5·(-2)
Δ = 3640
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:

$\sqrt{\Delta}=\sqrt{3640}=\sqrt{4*910}=\sqrt{4}*\sqrt{910}=2\sqrt{910}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{910}}{2*5}=\frac{-60-2\sqrt{910}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{910}}{2*5}=\frac{-60+2\sqrt{910}}{10}
$