(x+4)(4x-3)+x=186

Solution for (x+4)(4x-3)+x=186 equation:

(x+4)(4x-3)+x=186

We move all terms to the left:

(x+4)(4x-3)+x-(186)=0

We add all the numbers together, and all the variables

x+(x+4)(4x-3)-186=0

We multiply parentheses ..

(+4x^2-3x+16x-12)+x-186=0

We get rid of parentheses

4x^2-3x+16x+x-12-186=0

We add all the numbers together, and all the variables

4x^2+14x-198=0

a = 4; b = 14; c = -198;
Δ = b2-4ac
Δ = 142-4·4·(-198)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-58}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+58}{2*4}=\frac{44}{8}
=5+1/2
$