-3(x+9)10x=34

Solution for -3(x+9)10x=34 equation:

-3(x+9)10x=34

We move all terms to the left:

-3(x+9)10x-(34)=0

We multiply parentheses

-30x^2-270x-34=0

a = -30; b = -270; c = -34;
Δ = b2-4ac
Δ = -2702-4·(-30)·(-34)
Δ = 68820
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:

$\sqrt{\Delta}=\sqrt{68820}=\sqrt{4*17205}=\sqrt{4}*\sqrt{17205}=2\sqrt{17205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{17205}}{2*-30}=\frac{270-2\sqrt{17205}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{17205}}{2*-30}=\frac{270+2\sqrt{17205}}{-60}
$