102+x(4x+6)=180

Solution for 102+x(4x+6)=180 equation:

102+x(4x+6)=180

We move all terms to the left:

102+x(4x+6)-(180)=0

We add all the numbers together, and all the variables

x(4x+6)-78=0

We multiply parentheses

4x^2+6x-78=0

a = 4; b = 6; c = -78;
Δ = b2-4ac
Δ = 62-4·4·(-78)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{321}}{2*4}=\frac{-6-2\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{321}}{2*4}=\frac{-6+2\sqrt{321}}{8}
$