6x^2=27x^2-105x

Solution for 6x^2=27x^2-105x equation:

6x^2=27x^2-105x

We move all terms to the left:

6x^2-(27x^2-105x)=0

We get rid of parentheses

6x^2-27x^2+105x=0

We add all the numbers together, and all the variables

-21x^2+105x=0

a = -21; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·(-21)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-105}{2*-21}=\frac{-210}{-42}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*-21}=\frac{0}{-42}
=0
$