(17x+14)(4x-2)=180

Solution for (17x+14)(4x-2)=180 equation:

(17x+14)(4x-2)=180

We move all terms to the left:

(17x+14)(4x-2)-(180)=0

We multiply parentheses ..

(+68x^2-34x+56x-28)-180=0

We get rid of parentheses

68x^2-34x+56x-28-180=0

We add all the numbers together, and all the variables

68x^2+22x-208=0

a = 68; b = 22; c = -208;
Δ = b2-4ac
Δ = 222-4·68·(-208)
Δ = 57060
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:

$\sqrt{\Delta}=\sqrt{57060}=\sqrt{36*1585}=\sqrt{36}*\sqrt{1585}=6\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{1585}}{2*68}=\frac{-22-6\sqrt{1585}}{136}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{1585}}{2*68}=\frac{-22+6\sqrt{1585}}{136}
$