F(x)=-3/4x+21

Solution for F(x)=-3/4x+21 equation:

(F)=-3/4F+21

We move all terms to the left:

(F)-(-3/4F+21)=0


Domain of the equation: 4F+21)!=0

F∈R


We get rid of parentheses

F+3/4F-21=0

We multiply all the terms by the denominator


F*4F-21*4F+3=0

Wy multiply elements

4F^2-84F+3=0

a = 4; b = -84; c = +3;
Δ = b2-4ac
Δ = -842-4·4·3
Δ = 7008
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:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{438}}{2*4}=\frac{84-4\sqrt{438}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{438}}{2*4}=\frac{84+4\sqrt{438}}{8}
$