2x(x+1)=7-3(x-1)

Solution for 2x(x+1)=7-3(x-1) equation:

2x(x+1)=7-3(x-1)

We move all terms to the left:

2x(x+1)-(7-3(x-1))=0

We multiply parentheses

2x^2+2x-(7-3(x-1))=0


We calculate terms in parentheses: -(7-3(x-1)), so:

7-3(x-1)

determiningTheFunctionDomain
-3(x-1)+7

We multiply parentheses

-3x+3+7

We add all the numbers together, and all the variables

-3x+10

Back to the equation:

-(-3x+10)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x-10=0

a = 2; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·2·(-10)
Δ = 105
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{105}}{2*2}=\frac{-5-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{105}}{2*2}=\frac{-5+\sqrt{105}}{4}
$