-2x(10+6x)+10=-34

Solution for -2x(10+6x)+10=-34 equation:

-2x(10+6x)+10=-34

We move all terms to the left:

-2x(10+6x)+10-(-34)=0

We add all the numbers together, and all the variables

-2x(6x+10)+10-(-34)=0

We add all the numbers together, and all the variables

-2x(6x+10)+44=0

We multiply parentheses

-12x^2-20x+44=0

a = -12; b = -20; c = +44;
Δ = b2-4ac
Δ = -202-4·(-12)·44
Δ = 2512
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:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{157}}{2*-12}=\frac{20-4\sqrt{157}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{157}}{2*-12}=\frac{20+4\sqrt{157}}{-24}
$