F(x)=5/6x+10

Solution for F(x)=5/6x+10 equation:

(F)=5/6F+10

We move all terms to the left:

(F)-(5/6F+10)=0


Domain of the equation: 6F+10)!=0

F∈R


We get rid of parentheses

F-5/6F-10=0

We multiply all the terms by the denominator


F*6F-10*6F-5=0

Wy multiply elements

6F^2-60F-5=0

a = 6; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·6·(-5)
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*6}=\frac{60-2\sqrt{930}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{930}}{2*6}=\frac{60+2\sqrt{930}}{12}
$