7-x(3x+9)=8x-6

Solution for 7-x(3x+9)=8x-6 equation:

7-x(3x+9)=8x-6

We move all terms to the left:

7-x(3x+9)-(8x-6)=0

We multiply parentheses

-3x^2-9x-(8x-6)+7=0

We get rid of parentheses

-3x^2-9x-8x+6+7=0

We add all the numbers together, and all the variables

-3x^2-17x+13=0

a = -3; b = -17; c = +13;
Δ = b2-4ac
Δ = -172-4·(-3)·13
Δ = 445
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{-(-17)-\sqrt{445}}{2*-3}=\frac{17-\sqrt{445}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{445}}{2*-3}=\frac{17+\sqrt{445}}{-6}
$