13/8x+7/2+9/4x+9=90

Solution for 13/8x+7/2+9/4x+9=90 equation:

13/8x+7/2+9/4x+9=90

We move all terms to the left:

13/8x+7/2+9/4x+9-(90)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
13/8x+9/4x+9-90+7/2=0

We add all the numbers together, and all the variables

13/8x+9/4x-81+7/2=0

We calculate fractions


896x^2/128x^2+208x/128x^2+288x/128x^2-81=0

We multiply all the terms by the denominator


896x^2+208x+288x-81*128x^2=0

We add all the numbers together, and all the variables

896x^2+496x-81*128x^2=0

Wy multiply elements

896x^2-10368x^2+496x=0

We add all the numbers together, and all the variables

-9472x^2+496x=0

a = -9472; b = 496; c = 0;
Δ = b2-4ac
Δ = 4962-4·(-9472)·0
Δ = 246016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{246016}=496$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(496)-496}{2*-9472}=\frac{-992}{-18944}
=31/592
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(496)+496}{2*-9472}=\frac{0}{-18944}
=0
$