F(x)=15/2x+3

Solution for F(x)=15/2x+3 equation:

(F)=15/2F+3

We move all terms to the left:

(F)-(15/2F+3)=0


Domain of the equation: 2F+3)!=0

F∈R


We get rid of parentheses

F-15/2F-3=0

We multiply all the terms by the denominator


F*2F-3*2F-15=0

Wy multiply elements

2F^2-6F-15=0

a = 2; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·2·(-15)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*2}=\frac{6-2\sqrt{39}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*2}=\frac{6+2\sqrt{39}}{4}
$