(6x^2-18)=(5x^2-3x)

Solution for (6x^2-18)=(5x^2-3x) equation:

(6x^2-18)=(5x^2-3x)

We move all terms to the left:

(6x^2-18)-((5x^2-3x))=0

We get rid of parentheses

6x^2-((5x^2-3x))-18=0


We calculate terms in parentheses: -((5x^2-3x)), so:

(5x^2-3x)

We get rid of parentheses

5x^2-3x

Back to the equation:

-(5x^2-3x)


We get rid of parentheses

6x^2-5x^2+3x-18=0

We add all the numbers together, and all the variables

x^2+3x-18=0

a = 1; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·1·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*1}=\frac{6}{2}
=3
$