(3x+7)(10x-22)=180

Solution for (3x+7)(10x-22)=180 equation:

(3x+7)(10x-22)=180

We move all terms to the left:

(3x+7)(10x-22)-(180)=0

We multiply parentheses ..

(+30x^2-66x+70x-154)-180=0

We get rid of parentheses

30x^2-66x+70x-154-180=0

We add all the numbers together, and all the variables

30x^2+4x-334=0

a = 30; b = 4; c = -334;
Δ = b2-4ac
Δ = 42-4·30·(-334)
Δ = 40096
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:

$\sqrt{\Delta}=\sqrt{40096}=\sqrt{16*2506}=\sqrt{16}*\sqrt{2506}=4\sqrt{2506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2506}}{2*30}=\frac{-4-4\sqrt{2506}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2506}}{2*30}=\frac{-4+4\sqrt{2506}}{60}
$