(2x+5)(x+3)=45

Solution for (2x+5)(x+3)=45 equation:

(2x+5)(x+3)=45

We move all terms to the left:

(2x+5)(x+3)-(45)=0

We multiply parentheses ..

(+2x^2+6x+5x+15)-45=0

We get rid of parentheses

2x^2+6x+5x+15-45=0

We add all the numbers together, and all the variables

2x^2+11x-30=0

a = 2; b = 11; c = -30;
Δ = b2-4ac
Δ = 112-4·2·(-30)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*2}=\frac{8}{4}
=2
$