10x^2+6x=6x^2+18x

Solution for 10x^2+6x=6x^2+18x equation:

10x^2+6x=6x^2+18x

We move all terms to the left:

10x^2+6x-(6x^2+18x)=0

We get rid of parentheses

10x^2-6x^2+6x-18x=0

We add all the numbers together, and all the variables

4x^2-12x=0

a = 4; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·4·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*4}=\frac{24}{8}
=3
$