(7x-14)(2x+5)=180

Solution for (7x-14)(2x+5)=180 equation:

(7x-14)(2x+5)=180

We move all terms to the left:

(7x-14)(2x+5)-(180)=0

We multiply parentheses ..

(+14x^2+35x-28x-70)-180=0

We get rid of parentheses

14x^2+35x-28x-70-180=0

We add all the numbers together, and all the variables

14x^2+7x-250=0

a = 14; b = 7; c = -250;
Δ = b2-4ac
Δ = 72-4·14·(-250)
Δ = 14049
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:

$\sqrt{\Delta}=\sqrt{14049}=\sqrt{9*1561}=\sqrt{9}*\sqrt{1561}=3\sqrt{1561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{1561}}{2*14}=\frac{-7-3\sqrt{1561}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{1561}}{2*14}=\frac{-7+3\sqrt{1561}}{28}
$