F(x)=3x-2/4x+7

Solution for F(x)=3x-2/4x+7 equation:

(F)=3F-2/4F+7

We move all terms to the left:

(F)-(3F-2/4F+7)=0


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

F∈R


We get rid of parentheses

F-3F+2/4F-7=0

We multiply all the terms by the denominator


F*4F-3F*4F-7*4F+2=0

Wy multiply elements

4F^2-12F^2-28F+2=0

We add all the numbers together, and all the variables

-8F^2-28F+2=0

a = -8; b = -28; c = +2;
Δ = b2-4ac
Δ = -282-4·(-8)·2
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{53}}{2*-8}=\frac{28-4\sqrt{53}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{53}}{2*-8}=\frac{28+4\sqrt{53}}{-16}
$