(2x+46)(3x+6)=90

Solution for (2x+46)(3x+6)=90 equation:

(2x+46)(3x+6)=90

We move all terms to the left:

(2x+46)(3x+6)-(90)=0

We multiply parentheses ..

(+6x^2+12x+138x+276)-90=0

We get rid of parentheses

6x^2+12x+138x+276-90=0

We add all the numbers together, and all the variables

6x^2+150x+186=0

a = 6; b = 150; c = +186;
Δ = b2-4ac
Δ = 1502-4·6·186
Δ = 18036
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:

$\sqrt{\Delta}=\sqrt{18036}=\sqrt{36*501}=\sqrt{36}*\sqrt{501}=6\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-6\sqrt{501}}{2*6}=\frac{-150-6\sqrt{501}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+6\sqrt{501}}{2*6}=\frac{-150+6\sqrt{501}}{12}
$