12(7.5)=(2x+1)(x+6)

Solution for 12(7.5)=(2x+1)(x+6) equation:

12(7.5)=(2x+1)(x+6)

We move all terms to the left:

12(7.5)-((2x+1)(x+6))=0

We add all the numbers together, and all the variables

-((2x+1)(x+6))+90=0

We multiply parentheses ..

-((+2x^2+12x+x+6))+90=0


We calculate terms in parentheses: -((+2x^2+12x+x+6)), so:

(+2x^2+12x+x+6)

We get rid of parentheses

2x^2+12x+x+6

We add all the numbers together, and all the variables

2x^2+13x+6

Back to the equation:

-(2x^2+13x+6)


We get rid of parentheses

-2x^2-13x-6+90=0

We add all the numbers together, and all the variables

-2x^2-13x+84=0

a = -2; b = -13; c = +84;
Δ = b2-4ac
Δ = -132-4·(-2)·84
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*-2}=\frac{42}{-4}
=-10+1/2
$