21/8x+30=513x

Solution for 21/8x+30=513x equation:

21/8x+30=513x

We move all terms to the left:

21/8x+30-(513x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-513x+21/8x+30=0

We multiply all the terms by the denominator


-513x*8x+30*8x+21=0

Wy multiply elements

-4104x^2+240x+21=0

a = -4104; b = 240; c = +21;
Δ = b2-4ac
Δ = 2402-4·(-4104)·21
Δ = 402336
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:

$\sqrt{\Delta}=\sqrt{402336}=\sqrt{144*2794}=\sqrt{144}*\sqrt{2794}=12\sqrt{2794}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-12\sqrt{2794}}{2*-4104}=\frac{-240-12\sqrt{2794}}{-8208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+12\sqrt{2794}}{2*-4104}=\frac{-240+12\sqrt{2794}}{-8208}
$