F(x)=10/5x-3

Solution for F(x)=10/5x-3 equation:

(F)=10/5F-3

We move all terms to the left:

(F)-(10/5F-3)=0


Domain of the equation: 5F-3)!=0

F∈R


We get rid of parentheses

F-10/5F+3=0

We multiply all the terms by the denominator


F*5F+3*5F-10=0

Wy multiply elements

5F^2+15F-10=0

a = 5; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·5·(-10)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{17}}{2*5}=\frac{-15-5\sqrt{17}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{17}}{2*5}=\frac{-15+5\sqrt{17}}{10}
$