6x(-2x+5)=-42

Solution for 6x(-2x+5)=-42 equation:

6x(-2x+5)=-42

We move all terms to the left:

6x(-2x+5)-(-42)=0

We add all the numbers together, and all the variables

6x(-2x+5)+42=0

We multiply parentheses

-12x^2+30x+42=0

a = -12; b = 30; c = +42;
Δ = b2-4ac
Δ = 302-4·(-12)·42
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-54}{2*-12}=\frac{-84}{-24}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+54}{2*-12}=\frac{24}{-24}
=-1
$