F(x)=-3/2x+175

Solution for F(x)=-3/2x+175 equation:

(F)=-3/2F+175

We move all terms to the left:

(F)-(-3/2F+175)=0


Domain of the equation: 2F+175)!=0

F∈R


We get rid of parentheses

F+3/2F-175=0

We multiply all the terms by the denominator


F*2F-175*2F+3=0

Wy multiply elements

2F^2-350F+3=0

a = 2; b = -350; c = +3;
Δ = b2-4ac
Δ = -3502-4·2·3
Δ = 122476
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:

$\sqrt{\Delta}=\sqrt{122476}=\sqrt{4*30619}=\sqrt{4}*\sqrt{30619}=2\sqrt{30619}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30619}}{2*2}=\frac{350-2\sqrt{30619}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30619}}{2*2}=\frac{350+2\sqrt{30619}}{4}
$