2x(x+1)=-3(x-2)

Solution for 2x(x+1)=-3(x-2) equation:

2x(x+1)=-3(x-2)

We move all terms to the left:

2x(x+1)-(-3(x-2))=0

We multiply parentheses

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


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

-3(x-2)

We multiply parentheses

-3x+6

Back to the equation:

-(-3x+6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x-6=0

a = 2; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·2·(-6)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{73}}{2*2}=\frac{-5-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*2}=\frac{-5+\sqrt{73}}{4}
$