x^2/4x-5+16/5-4x=0

Solution for x^2/4x-5+16/5-4x=0 equation:

x^2/4x-5+16/5-4x=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


5x^2/20x-4x+64x/20x-5=0

We multiply all the terms by the denominator


5x^2-4x*20x+64x-5*20x=0

We add all the numbers together, and all the variables

5x^2+64x-4x*20x-5*20x=0

Wy multiply elements

5x^2-80x^2+64x-100x=0

We add all the numbers together, and all the variables

-75x^2-36x=0

a = -75; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-75)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-75}=\frac{0}{-150}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-75}=\frac{72}{-150}
=-12/25
$