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

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

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

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4F^2-8F^2+28F-3=0

We add all the numbers together, and all the variables

-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}
$