2(3x-5)=x2-4

Solution for 2(3x-5)=x2-4 equation:

2(3x-5)=x2-4

We move all terms to the left:

2(3x-5)-(x2-4)=0

We add all the numbers together, and all the variables

-(+x^2-4)+2(3x-5)=0

We multiply parentheses

-(+x^2-4)+6x-10=0

We get rid of parentheses

-x^2+6x+4-10=0

We add all the numbers together, and all the variables

-1x^2+6x-6=0

a = -1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·(-1)·(-6)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*-1}=\frac{-6-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*-1}=\frac{-6+2\sqrt{3}}{-2}
$