F(x)=3/4x-150

Solution for F(x)=3/4x-150 equation:

(F)=3/4F-150

We move all terms to the left:

(F)-(3/4F-150)=0


Domain of the equation: 4F-150)!=0

F∈R


We get rid of parentheses

F-3/4F+150=0

We multiply all the terms by the denominator


F*4F+150*4F-3=0

Wy multiply elements

4F^2+600F-3=0

a = 4; b = 600; c = -3;
Δ = b2-4ac
Δ = 6002-4·4·(-3)
Δ = 360048
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:

$\sqrt{\Delta}=\sqrt{360048}=\sqrt{16*22503}=\sqrt{16}*\sqrt{22503}=4\sqrt{22503}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-4\sqrt{22503}}{2*4}=\frac{-600-4\sqrt{22503}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+4\sqrt{22503}}{2*4}=\frac{-600+4\sqrt{22503}}{8}
$