F(x)=-3/10x-8

Solution for F(x)=-3/10x-8 equation:

(F)=-3/10F-8

We move all terms to the left:

(F)-(-3/10F-8)=0


Domain of the equation: 10F-8)!=0

F∈R


We get rid of parentheses

F+3/10F+8=0

We multiply all the terms by the denominator


F*10F+8*10F+3=0

Wy multiply elements

10F^2+80F+3=0

a = 10; b = 80; c = +3;
Δ = b2-4ac
Δ = 802-4·10·3
Δ = 6280
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:

$\sqrt{\Delta}=\sqrt{6280}=\sqrt{4*1570}=\sqrt{4}*\sqrt{1570}=2\sqrt{1570}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1570}}{2*10}=\frac{-80-2\sqrt{1570}}{20}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1570}}{2*10}=\frac{-80+2\sqrt{1570}}{20}
$