9+6(10-7x)x=2

Solution for 9+6(10-7x)x=2 equation:

9+6(10-7x)x=2

We move all terms to the left:

9+6(10-7x)x-(2)=0

We add all the numbers together, and all the variables

6(-7x+10)x+9-2=0

We add all the numbers together, and all the variables

6(-7x+10)x+7=0

We multiply parentheses

-42x^2+60x+7=0

a = -42; b = 60; c = +7;
Δ = b2-4ac
Δ = 602-4·(-42)·7
Δ = 4776
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:

$\sqrt{\Delta}=\sqrt{4776}=\sqrt{4*1194}=\sqrt{4}*\sqrt{1194}=2\sqrt{1194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{1194}}{2*-42}=\frac{-60-2\sqrt{1194}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{1194}}{2*-42}=\frac{-60+2\sqrt{1194}}{-84}
$