(x)/8x+3=4x+13

Solution for (x)/8x+3=4x+13 equation:

(x)/8x+3=4x+13

We move all terms to the left:

(x)/8x+3-(4x+13)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

x/8x-4x-13+3=0

We multiply all the terms by the denominator


x-4x*8x-13*8x+3*8x=0

Wy multiply elements

-32x^2+x-104x+24x=0

We add all the numbers together, and all the variables

-32x^2-79x=0

a = -32; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·(-32)·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*-32}=\frac{158}{-64}
=-2+15/32
$