(14x+2)11x+3=180

Solution for (14x+2)11x+3=180 equation:

(14x+2)11x+3=180

We move all terms to the left:

(14x+2)11x+3-(180)=0

We add all the numbers together, and all the variables

(14x+2)11x-177=0

We multiply parentheses

154x^2+22x-177=0

a = 154; b = 22; c = -177;
Δ = b2-4ac
Δ = 222-4·154·(-177)
Δ = 109516
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:

$\sqrt{\Delta}=\sqrt{109516}=\sqrt{4*27379}=\sqrt{4}*\sqrt{27379}=2\sqrt{27379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{27379}}{2*154}=\frac{-22-2\sqrt{27379}}{308}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{27379}}{2*154}=\frac{-22+2\sqrt{27379}}{308}
$