187=(2x+3)(x+4)

Solution for 187=(2x+3)(x+4) equation:

187=(2x+3)(x+4)

We move all terms to the left:

187-((2x+3)(x+4))=0

We multiply parentheses ..

-((+2x^2+8x+3x+12))+187=0


We calculate terms in parentheses: -((+2x^2+8x+3x+12)), so:

(+2x^2+8x+3x+12)

We get rid of parentheses

2x^2+8x+3x+12

We add all the numbers together, and all the variables

2x^2+11x+12

Back to the equation:

-(2x^2+11x+12)


We get rid of parentheses

-2x^2-11x-12+187=0

We add all the numbers together, and all the variables

-2x^2-11x+175=0

a = -2; b = -11; c = +175;
Δ = b2-4ac
Δ = -112-4·(-2)·175
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-39}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+39}{2*-2}=\frac{50}{-4}
=-12+1/2
$