3(x-2)(x+5)=(x-2)(x+1)+3

Solution for 3(x-2)(x+5)=(x-2)(x+1)+3 equation:

3(x-2)(x+5)=(x-2)(x+1)+3

We move all terms to the left:

3(x-2)(x+5)-((x-2)(x+1)+3)=0

We multiply parentheses ..

3(+x^2+5x-2x-10)-((x-2)(x+1)+3)=0


We calculate terms in parentheses: -((x-2)(x+1)+3), so:

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

We multiply parentheses ..

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

We get rid of parentheses

x^2+x-2x-2+3

We add all the numbers together, and all the variables

x^2-1x+1

Back to the equation:

-(x^2-1x+1)


We multiply parentheses

3x^2+15x-6x-(x^2-1x+1)-30=0

We get rid of parentheses

3x^2-x^2+15x-6x+1x-1-30=0

We add all the numbers together, and all the variables

2x^2+10x-31=0

a = 2; b = 10; c = -31;
Δ = b2-4ac
Δ = 102-4·2·(-31)
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{87}}{2*2}=\frac{-10-2\sqrt{87}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{87}}{2*2}=\frac{-10+2\sqrt{87}}{4}
$