16x-25/4x+5=59

Solution for 16x-25/4x+5=59 equation:

16x-25/4x+5=59

We move all terms to the left:

16x-25/4x+5-(59)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

16x-25/4x-54=0

We multiply all the terms by the denominator


16x*4x-54*4x-25=0

Wy multiply elements

64x^2-216x-25=0

a = 64; b = -216; c = -25;
Δ = b2-4ac
Δ = -2162-4·64·(-25)
Δ = 53056
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:

$\sqrt{\Delta}=\sqrt{53056}=\sqrt{64*829}=\sqrt{64}*\sqrt{829}=8\sqrt{829}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-8\sqrt{829}}{2*64}=\frac{216-8\sqrt{829}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+8\sqrt{829}}{2*64}=\frac{216+8\sqrt{829}}{128}
$