(-9/4x-19)=7/2x+27

Solution for (-9/4x-19)=7/2x+27 equation:

(-9/4x-19)=7/2x+27

We move all terms to the left:

(-9/4x-19)-(7/2x+27)=0


Domain of the equation: 4x-19)!=0

x∈R



Domain of the equation: 2x+27)!=0

x∈R


We get rid of parentheses

-9/4x-7/2x-19-27=0

We calculate fractions


(-18x)/8x^2+(-28x)/8x^2-19-27=0

We add all the numbers together, and all the variables

(-18x)/8x^2+(-28x)/8x^2-46=0

We multiply all the terms by the denominator


(-18x)+(-28x)-46*8x^2=0

Wy multiply elements

-368x^2+(-18x)+(-28x)=0

We get rid of parentheses

-368x^2-18x-28x=0

We add all the numbers together, and all the variables

-368x^2-46x=0

a = -368; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·(-368)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*-368}=\frac{0}{-736}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*-368}=\frac{92}{-736}
=-1/8
$