(2*3)+(x*x)=6x2

Solution for (2*3)+(x*x)=6x2 equation:

(2*3)+(x*x)=6x^2

We move all terms to the left:

(2*3)+(x*x)-(6x^2)=0

determiningTheFunctionDomain
-6x^2+(x*x)+(2*3)=0

We add all the numbers together, and all the variables

-6x^2+(+x*x)+6=0

We get rid of parentheses

-6x^2+x*x+6=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2+6=0

a = -5; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-5)·6
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-5}=\frac{0-2\sqrt{30}}{-10}
=-\frac{2\sqrt{30}}{-10}
=-\frac{\sqrt{30}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-5}=\frac{0+2\sqrt{30}}{-10}
=\frac{2\sqrt{30}}{-10}
=\frac{\sqrt{30}}{-5}
$