x(12x-15)=21x

Solution for x(12x-15)=21x equation:

x(12x-15)=21x

We move all terms to the left:

x(12x-15)-(21x)=0

We add all the numbers together, and all the variables

-21x+x(12x-15)=0

We multiply parentheses

12x^2-21x-15x=0

We add all the numbers together, and all the variables

12x^2-36x=0

a = 12; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·12·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*12}=\frac{72}{24}
=3
$