5x+8=25/4x

Solution for 5x+8=25/4x equation:

5x+8=25/4x

We move all terms to the left:

5x+8-(25/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+25/4x)+8=0

We get rid of parentheses

5x-25/4x+8=0

We multiply all the terms by the denominator


5x*4x+8*4x-25=0

Wy multiply elements

20x^2+32x-25=0

a = 20; b = 32; c = -25;
Δ = b2-4ac
Δ = 322-4·20·(-25)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{21}}{2*20}=\frac{-32-12\sqrt{21}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{21}}{2*20}=\frac{-32+12\sqrt{21}}{40}
$