/4x+15=x-3

Solution for /4x+15=x-3 equation:

/4x+15=x-3

We move all terms to the left:

/4x+15-(x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

/4x-x+3+15=0

We multiply all the terms by the denominator


-x*4x+3*4x+15*4x+=0

We add all the numbers together, and all the variables

-x*4x+3*4x+15*4x=0

Wy multiply elements

-4x^2+12x+60x=0

We add all the numbers together, and all the variables

-4x^2+72x=0

a = -4; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-4)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-4}=\frac{-144}{-8}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-4}=\frac{0}{-8}
=0
$