F(x)=-13/21x+13

Solution for F(x)=-13/21x+13 equation:

(F)=-13/21F+13

We move all terms to the left:

(F)-(-13/21F+13)=0


Domain of the equation: 21F+13)!=0

F∈R


We get rid of parentheses

F+13/21F-13=0

We multiply all the terms by the denominator


F*21F-13*21F+13=0

Wy multiply elements

21F^2-273F+13=0

a = 21; b = -273; c = +13;
Δ = b2-4ac
Δ = -2732-4·21·13
Δ = 73437
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-273)-\sqrt{73437}}{2*21}=\frac{273-\sqrt{73437}}{42}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-273)+\sqrt{73437}}{2*21}=\frac{273+\sqrt{73437}}{42}
$