(3x-14)(x+34)=180

Solution for (3x-14)(x+34)=180 equation:

(3x-14)(x+34)=180

We move all terms to the left:

(3x-14)(x+34)-(180)=0

We multiply parentheses ..

(+3x^2+102x-14x-476)-180=0

We get rid of parentheses

3x^2+102x-14x-476-180=0

We add all the numbers together, and all the variables

3x^2+88x-656=0

a = 3; b = 88; c = -656;
Δ = b2-4ac
Δ = 882-4·3·(-656)
Δ = 15616
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:

$\sqrt{\Delta}=\sqrt{15616}=\sqrt{256*61}=\sqrt{256}*\sqrt{61}=16\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-16\sqrt{61}}{2*3}=\frac{-88-16\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+16\sqrt{61}}{2*3}=\frac{-88+16\sqrt{61}}{6}
$