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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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


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

2(-2x+3)

We multiply parentheses

-4x+6

Back to the equation:

-(-4x+6)


We get rid of parentheses

x^2-5x+4x-6=0

We add all the numbers together, and all the variables

x^2-1x-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$