(6x+15)(7x-6)=180

Solution for (6x+15)(7x-6)=180 equation:

(6x+15)(7x-6)=180

We move all terms to the left:

(6x+15)(7x-6)-(180)=0

We multiply parentheses ..

(+42x^2-36x+105x-90)-180=0

We get rid of parentheses

42x^2-36x+105x-90-180=0

We add all the numbers together, and all the variables

42x^2+69x-270=0

a = 42; b = 69; c = -270;
Δ = b2-4ac
Δ = 692-4·42·(-270)
Δ = 50121
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:

$\sqrt{\Delta}=\sqrt{50121}=\sqrt{9*5569}=\sqrt{9}*\sqrt{5569}=3\sqrt{5569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{5569}}{2*42}=\frac{-69-3\sqrt{5569}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{5569}}{2*42}=\frac{-69+3\sqrt{5569}}{84}
$