F(x)=-3/4x+7

Solution for F(x)=-3/4x+7 equation:

(F)=-3/4F+7

We move all terms to the left:

(F)-(-3/4F+7)=0


Domain of the equation: 4F+7)!=0

F∈R


We get rid of parentheses

F+3/4F-7=0

We multiply all the terms by the denominator


F*4F-7*4F+3=0

Wy multiply elements

4F^2-28F+3=0

a = 4; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·4·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{46}}{2*4}=\frac{28-4\sqrt{46}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{46}}{2*4}=\frac{28+4\sqrt{46}}{8}
$