(10x+12)(4x+132)=186

Solution for (10x+12)(4x+132)=186 equation:

(10x+12)(4x+132)=186

We move all terms to the left:

(10x+12)(4x+132)-(186)=0

We multiply parentheses ..

(+40x^2+1320x+48x+1584)-186=0

We get rid of parentheses

40x^2+1320x+48x+1584-186=0

We add all the numbers together, and all the variables

40x^2+1368x+1398=0

a = 40; b = 1368; c = +1398;
Δ = b2-4ac
Δ = 13682-4·40·1398
Δ = 1647744
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:

$\sqrt{\Delta}=\sqrt{1647744}=\sqrt{64*25746}=\sqrt{64}*\sqrt{25746}=8\sqrt{25746}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1368)-8\sqrt{25746}}{2*40}=\frac{-1368-8\sqrt{25746}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1368)+8\sqrt{25746}}{2*40}=\frac{-1368+8\sqrt{25746}}{80}
$