F(x)=3/2x-10

Solution for F(x)=3/2x-10 equation:

(F)=3/2F-10

We move all terms to the left:

(F)-(3/2F-10)=0


Domain of the equation: 2F-10)!=0

F∈R


We get rid of parentheses

F-3/2F+10=0

We multiply all the terms by the denominator


F*2F+10*2F-3=0

Wy multiply elements

2F^2+20F-3=0

a = 2; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·2·(-3)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{106}}{2*2}=\frac{-20-2\sqrt{106}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{106}}{2*2}=\frac{-20+2\sqrt{106}}{4}
$