-5x(1+2x)-8x=-6(x+7)+1

Solution for -5x(1+2x)-8x=-6(x+7)+1 equation:

-5x(1+2x)-8x=-6(x+7)+1

We move all terms to the left:

-5x(1+2x)-8x-(-6(x+7)+1)=0

We add all the numbers together, and all the variables

-5x(2x+1)-8x-(-6(x+7)+1)=0

We add all the numbers together, and all the variables

-8x-5x(2x+1)-(-6(x+7)+1)=0

We multiply parentheses

-10x^2-8x-5x-(-6(x+7)+1)=0


We calculate terms in parentheses: -(-6(x+7)+1), so:

-6(x+7)+1

We multiply parentheses

-6x-42+1

We add all the numbers together, and all the variables

-6x-41

Back to the equation:

-(-6x-41)


We add all the numbers together, and all the variables

-10x^2-13x-(-6x-41)=0

We get rid of parentheses

-10x^2-13x+6x+41=0

We add all the numbers together, and all the variables

-10x^2-7x+41=0

a = -10; b = -7; c = +41;
Δ = b2-4ac
Δ = -72-4·(-10)·41
Δ = 1689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1689}}{2*-10}=\frac{7-\sqrt{1689}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1689}}{2*-10}=\frac{7+\sqrt{1689}}{-20}
$