27x-30=51/7x

Solution for 27x-30=51/7x equation:

27x-30=51/7x

We move all terms to the left:

27x-30-(51/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

27x-(+51/7x)-30=0

We get rid of parentheses

27x-51/7x-30=0

We multiply all the terms by the denominator


27x*7x-30*7x-51=0

Wy multiply elements

189x^2-210x-51=0

a = 189; b = -210; c = -51;
Δ = b2-4ac
Δ = -2102-4·189·(-51)
Δ = 82656
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:

$\sqrt{\Delta}=\sqrt{82656}=\sqrt{144*574}=\sqrt{144}*\sqrt{574}=12\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-12\sqrt{574}}{2*189}=\frac{210-12\sqrt{574}}{378}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+12\sqrt{574}}{2*189}=\frac{210+12\sqrt{574}}{378}
$