4x(3x-36+1)=10

Solution for 4x(3x-36+1)=10 equation:

4x(3x-36+1)=10

We move all terms to the left:

4x(3x-36+1)-(10)=0

We add all the numbers together, and all the variables

4x(3x-35)-10=0

We multiply parentheses

12x^2-140x-10=0

a = 12; b = -140; c = -10;
Δ = b2-4ac
Δ = -1402-4·12·(-10)
Δ = 20080
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:

$\sqrt{\Delta}=\sqrt{20080}=\sqrt{16*1255}=\sqrt{16}*\sqrt{1255}=4\sqrt{1255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1255}}{2*12}=\frac{140-4\sqrt{1255}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1255}}{2*12}=\frac{140+4\sqrt{1255}}{24}
$