(3x+6)(4x+21)=90

Solution for (3x+6)(4x+21)=90 equation:

(3x+6)(4x+21)=90

We move all terms to the left:

(3x+6)(4x+21)-(90)=0

We multiply parentheses ..

(+12x^2+63x+24x+126)-90=0

We get rid of parentheses

12x^2+63x+24x+126-90=0

We add all the numbers together, and all the variables

12x^2+87x+36=0

a = 12; b = 87; c = +36;
Δ = b2-4ac
Δ = 872-4·12·36
Δ = 5841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5841}=\sqrt{9*649}=\sqrt{9}*\sqrt{649}=3\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-3\sqrt{649}}{2*12}=\frac{-87-3\sqrt{649}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+3\sqrt{649}}{2*12}=\frac{-87+3\sqrt{649}}{24}
$