F(x)=-7/5x-12

Solution for F(x)=-7/5x-12 equation:

(F)=-7/5F-12

We move all terms to the left:

(F)-(-7/5F-12)=0


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

F∈R


We get rid of parentheses

F+7/5F+12=0

We multiply all the terms by the denominator


F*5F+12*5F+7=0

Wy multiply elements

5F^2+60F+7=0

a = 5; b = 60; c = +7;
Δ = b2-4ac
Δ = 602-4·5·7
Δ = 3460
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:

$\sqrt{\Delta}=\sqrt{3460}=\sqrt{4*865}=\sqrt{4}*\sqrt{865}=2\sqrt{865}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{865}}{2*5}=\frac{-60-2\sqrt{865}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{865}}{2*5}=\frac{-60+2\sqrt{865}}{10}
$