(4x+1)(6x+9)=90

Solution for (4x+1)(6x+9)=90 equation:

(4x+1)(6x+9)=90

We move all terms to the left:

(4x+1)(6x+9)-(90)=0

We multiply parentheses ..

(+24x^2+36x+6x+9)-90=0

We get rid of parentheses

24x^2+36x+6x+9-90=0

We add all the numbers together, and all the variables

24x^2+42x-81=0

a = 24; b = 42; c = -81;
Δ = b2-4ac
Δ = 422-4·24·(-81)
Δ = 9540
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:

$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{265}}{2*24}=\frac{-42-6\sqrt{265}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{265}}{2*24}=\frac{-42+6\sqrt{265}}{48}
$