F(x)=4/7x-10

Solution for F(x)=4/7x-10 equation:

(F)=4/7F-10

We move all terms to the left:

(F)-(4/7F-10)=0


Domain of the equation: 7F-10)!=0

F∈R


We get rid of parentheses

F-4/7F+10=0

We multiply all the terms by the denominator


F*7F+10*7F-4=0

Wy multiply elements

7F^2+70F-4=0

a = 7; b = 70; c = -4;
Δ = b2-4ac
Δ = 702-4·7·(-4)
Δ = 5012
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:

$\sqrt{\Delta}=\sqrt{5012}=\sqrt{4*1253}=\sqrt{4}*\sqrt{1253}=2\sqrt{1253}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1253}}{2*7}=\frac{-70-2\sqrt{1253}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1253}}{2*7}=\frac{-70+2\sqrt{1253}}{14}
$