-12=x(3x-35)

Solution for -12=x(3x-35) equation:

-12=x(3x-35)

We move all terms to the left:

-12-(x(3x-35))=0


We calculate terms in parentheses: -(x(3x-35)), so:

x(3x-35)

We multiply parentheses

3x^2-35x

Back to the equation:

-(3x^2-35x)


We get rid of parentheses

-3x^2+35x-12=0

a = -3; b = 35; c = -12;
Δ = b2-4ac
Δ = 352-4·(-3)·(-12)
Δ = 1081
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{-(35)-\sqrt{1081}}{2*-3}=\frac{-35-\sqrt{1081}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1081}}{2*-3}=\frac{-35+\sqrt{1081}}{-6}
$