-2(3x+5)-2x=5x(x+6)-1

Solution for -2(3x+5)-2x=5x(x+6)-1 equation:

-2(3x+5)-2x=5x(x+6)-1

We move all terms to the left:

-2(3x+5)-2x-(5x(x+6)-1)=0

We add all the numbers together, and all the variables

-2x-2(3x+5)-(5x(x+6)-1)=0

We multiply parentheses

-2x-6x-(5x(x+6)-1)-10=0


We calculate terms in parentheses: -(5x(x+6)-1), so:

5x(x+6)-1

We multiply parentheses

5x^2+30x-1

Back to the equation:

-(5x^2+30x-1)


We add all the numbers together, and all the variables

-8x-(5x^2+30x-1)-10=0

We get rid of parentheses

-5x^2-8x-30x+1-10=0

We add all the numbers together, and all the variables

-5x^2-38x-9=0

a = -5; b = -38; c = -9;
Δ = b2-4ac
Δ = -382-4·(-5)·(-9)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-4\sqrt{79}}{2*-5}=\frac{38-4\sqrt{79}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+4\sqrt{79}}{2*-5}=\frac{38+4\sqrt{79}}{-10}
$