2x(x+1)+3(x-2)=4(2-x)+6

Solution for 2x(x+1)+3(x-2)=4(2-x)+6 equation:

2x(x+1)+3(x-2)=4(2-x)+6

We move all terms to the left:

2x(x+1)+3(x-2)-(4(2-x)+6)=0

We add all the numbers together, and all the variables

2x(x+1)+3(x-2)-(4(-1x+2)+6)=0

We multiply parentheses

2x^2+2x+3x-(4(-1x+2)+6)-6=0


We calculate terms in parentheses: -(4(-1x+2)+6), so:

4(-1x+2)+6

We multiply parentheses

-4x+8+6

We add all the numbers together, and all the variables

-4x+14

Back to the equation:

-(-4x+14)


We add all the numbers together, and all the variables

2x^2+5x-(-4x+14)-6=0

We get rid of parentheses

2x^2+5x+4x-14-6=0

We add all the numbers together, and all the variables

2x^2+9x-20=0

a = 2; b = 9; c = -20;
Δ = b2-4ac
Δ = 92-4·2·(-20)
Δ = 241
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{-(9)-\sqrt{241}}{2*2}=\frac{-9-\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{241}}{2*2}=\frac{-9+\sqrt{241}}{4}
$