8x-9=(3x+21)x

Solution for 8x-9=(3x+21)x equation:

8x-9=(3x+21)x

We move all terms to the left:

8x-9-((3x+21)x)=0


We calculate terms in parentheses: -((3x+21)x), so:

(3x+21)x

We multiply parentheses

3x^2+21x

Back to the equation:

-(3x^2+21x)


We get rid of parentheses

-3x^2+8x-21x-9=0

We add all the numbers together, and all the variables

-3x^2-13x-9=0

a = -3; b = -13; c = -9;
Δ = b2-4ac
Δ = -132-4·(-3)·(-9)
Δ = 61
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{-(-13)-\sqrt{61}}{2*-3}=\frac{13-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{61}}{2*-3}=\frac{13+\sqrt{61}}{-6}
$