-4x=5((5/4)x)

Solution for -4x=5((5/4)x) equation:

-4x=5((5/4)x)

We move all terms to the left:

-4x-(5((5/4)x))=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-4x*4)x))-(5((+5=0

Wy multiply elements

-16x^2+5=0

a = -16; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-16)·5
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-16}=\frac{0-8\sqrt{5}}{-32}
=-\frac{8\sqrt{5}}{-32}
=-\frac{\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-16}=\frac{0+8\sqrt{5}}{-32}
=\frac{8\sqrt{5}}{-32}
=\frac{\sqrt{5}}{-4}
$