F(x)=6/5x+12

Solution for F(x)=6/5x+12 equation:

(F)=6/5F+12

We move all terms to the left:

(F)-(6/5F+12)=0


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

F∈R


We get rid of parentheses

F-6/5F-12=0

We multiply all the terms by the denominator


F*5F-12*5F-6=0

Wy multiply elements

5F^2-60F-6=0

a = 5; b = -60; c = -6;
Δ = b2-4ac
Δ = -602-4·5·(-6)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{930}}{2*5}=\frac{60-2\sqrt{930}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{930}}{2*5}=\frac{60+2\sqrt{930}}{10}
$