7x(4x+27)+x=180

Solution for 7x(4x+27)+x=180 equation:

7x(4x+27)+x=180

We move all terms to the left:

7x(4x+27)+x-(180)=0

We add all the numbers together, and all the variables

x+7x(4x+27)-180=0

We multiply parentheses

28x^2+x+189x-180=0

We add all the numbers together, and all the variables

28x^2+190x-180=0

a = 28; b = 190; c = -180;
Δ = b2-4ac
Δ = 1902-4·28·(-180)
Δ = 56260
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:

$\sqrt{\Delta}=\sqrt{56260}=\sqrt{4*14065}=\sqrt{4}*\sqrt{14065}=2\sqrt{14065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-2\sqrt{14065}}{2*28}=\frac{-190-2\sqrt{14065}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+2\sqrt{14065}}{2*28}=\frac{-190+2\sqrt{14065}}{56}
$