F(x)=5/2x-7

Solution for F(x)=5/2x-7 equation:

(F)=5/2F-7

We move all terms to the left:

(F)-(5/2F-7)=0


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

F∈R


We get rid of parentheses

F-5/2F+7=0

We multiply all the terms by the denominator


F*2F+7*2F-5=0

Wy multiply elements

2F^2+14F-5=0

a = 2; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·2·(-5)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{59}}{2*2}=\frac{-14-2\sqrt{59}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{59}}{2*2}=\frac{-14+2\sqrt{59}}{4}
$