F(x)=6x-11/2x+7

Solution for F(x)=6x-11/2x+7 equation:

(F)=6F-11/2F+7

We move all terms to the left:

(F)-(6F-11/2F+7)=0


Domain of the equation: 2F+7)!=0

F∈R


We get rid of parentheses

F-6F+11/2F-7=0

We multiply all the terms by the denominator


F*2F-6F*2F-7*2F+11=0

Wy multiply elements

2F^2-12F^2-14F+11=0

We add all the numbers together, and all the variables

-10F^2-14F+11=0

a = -10; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·(-10)·11
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{159}}{2*-10}=\frac{14-2\sqrt{159}}{-20}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{159}}{2*-10}=\frac{14+2\sqrt{159}}{-20}
$