5/8x+4=14x=

Solution for 5/8x+4=14x= equation:

5/8x+4=14x=

We move all terms to the left:

5/8x+4-(14x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-14x+5/8x+4=0

We multiply all the terms by the denominator


-14x*8x+4*8x+5=0

Wy multiply elements

-112x^2+32x+5=0

a = -112; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·(-112)·5
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{51}}{2*-112}=\frac{-32-8\sqrt{51}}{-224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{51}}{2*-112}=\frac{-32+8\sqrt{51}}{-224}
$