-3x*(5+-3/x)=51

Solution for -3x*(5+-3/x)=51 equation:

-3x(5+-3/x)=51

We move all terms to the left:

-3x(5+-3/x)-(51)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3x(-3/x)-51=0

We multiply parentheses

9x^2-51=0

a = 9; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·9·(-51)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{51}}{2*9}=\frac{0-6\sqrt{51}}{18}
=-\frac{6\sqrt{51}}{18}
=-\frac{\sqrt{51}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{51}}{2*9}=\frac{0+6\sqrt{51}}{18}
=\frac{6\sqrt{51}}{18}
=\frac{\sqrt{51}}{3}
$