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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2-2x+10=0

a = -3; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-3)·10
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-3}=\frac{2-2\sqrt{31}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-3}=\frac{2+2\sqrt{31}}{-6}
$