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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

(2x-3)(x+5)-3x+6-3=0

We multiply parentheses ..

(+2x^2+10x-3x-15)-3x+6-3=0

We add all the numbers together, and all the variables

(+2x^2+10x-3x-15)-3x+3=0

We get rid of parentheses

2x^2+10x-3x-3x-15+3=0

We add all the numbers together, and all the variables

2x^2+4x-12=0

a = 2; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·2·(-12)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*2}=\frac{-4-4\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*2}=\frac{-4+4\sqrt{7}}{4}
$