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

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

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

We move all terms to the left:

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


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

2(x-3)x

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+9x+5=0

a = -2; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-2)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-2}=\frac{2}{-4}
=-1/2
$