6x+5=1/4x+15

Solution for 6x+5=1/4x+15 equation:

6x+5=1/4x+15

We move all terms to the left:

6x+5-(1/4x+15)=0


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

x∈R


We get rid of parentheses

6x-1/4x-15+5=0

We multiply all the terms by the denominator


6x*4x-15*4x+5*4x-1=0

Wy multiply elements

24x^2-60x+20x-1=0

We add all the numbers together, and all the variables

24x^2-40x-1=0

a = 24; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·24·(-1)
Δ = 1696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*24}=\frac{40-4\sqrt{106}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*24}=\frac{40+4\sqrt{106}}{48}
$