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

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

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

We move all terms to the left:

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

We multiply parentheses

-10x^2+6x-35x-1=0

We add all the numbers together, and all the variables

-10x^2-29x-1=0

a = -10; b = -29; c = -1;
Δ = b2-4ac
Δ = -292-4·(-10)·(-1)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-3\sqrt{89}}{2*-10}=\frac{29-3\sqrt{89}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+3\sqrt{89}}{2*-10}=\frac{29+3\sqrt{89}}{-20}
$