(6-6x)(1/5)=-24

Solution for (6-6x)(1/5)=-24 equation:

(6-6x)(1/5)=-24

We move all terms to the left:

(6-6x)(1/5)-(-24)=0

We add all the numbers together, and all the variables

(-6x+6)(+1/5)-(-24)=0

We add all the numbers together, and all the variables

(-6x+6)(+1/5)+24=0

We multiply parentheses ..

(-6x^2+6*1/5)+24=0

We multiply all the terms by the denominator


(-6x^2+6*1+24*5)=0

We get rid of parentheses

-6x^2+6*1+24*5=0

We add all the numbers together, and all the variables

-6x^2+126=0

a = -6; b = 0; c = +126;
Δ = b2-4ac
Δ = 02-4·(-6)·126
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{21}}{2*-6}=\frac{0-12\sqrt{21}}{-12}
=-\frac{12\sqrt{21}}{-12}
=-\frac{\sqrt{21}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{21}}{2*-6}=\frac{0+12\sqrt{21}}{-12}
=\frac{12\sqrt{21}}{-12}
=\frac{\sqrt{21}}{-1}
$