F(x)=5/4x+15

Solution for F(x)=5/4x+15 equation:

(F)=5/4F+15

We move all terms to the left:

(F)-(5/4F+15)=0


Domain of the equation: 4F+15)!=0

F∈R


We get rid of parentheses

F-5/4F-15=0

We multiply all the terms by the denominator


F*4F-15*4F-5=0

Wy multiply elements

4F^2-60F-5=0

a = 4; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·4·(-5)
Δ = 3680
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:

$\sqrt{\Delta}=\sqrt{3680}=\sqrt{16*230}=\sqrt{16}*\sqrt{230}=4\sqrt{230}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{230}}{2*4}=\frac{60-4\sqrt{230}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{230}}{2*4}=\frac{60+4\sqrt{230}}{8}
$