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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-4x+5x-10)-3=0

We get rid of parentheses

2x^2-4x+5x-10-3=0

We add all the numbers together, and all the variables

2x^2+x-13=0

a = 2; b = 1; c = -13;
Δ = b2-4ac
Δ = 12-4·2·(-13)
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{-(1)-\sqrt{105}}{2*2}=\frac{-1-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{105}}{2*2}=\frac{-1+\sqrt{105}}{4}
$