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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

2x^2+x+12x+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{-42}{4}
=-10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+29}{2*2}=\frac{16}{4}
=4
$