(60-2x)(70-4x)=180

Solution for (60-2x)(70-4x)=180 equation:

(60-2x)(70-4x)=180

We move all terms to the left:

(60-2x)(70-4x)-(180)=0

We add all the numbers together, and all the variables

(-2x+60)(-4x+70)-180=0

We multiply parentheses ..

(+8x^2-140x-240x+4200)-180=0

We get rid of parentheses

8x^2-140x-240x+4200-180=0

We add all the numbers together, and all the variables

8x^2-380x+4020=0

a = 8; b = -380; c = +4020;
Δ = b2-4ac
Δ = -3802-4·8·4020
Δ = 15760
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:

$\sqrt{\Delta}=\sqrt{15760}=\sqrt{16*985}=\sqrt{16}*\sqrt{985}=4\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-4\sqrt{985}}{2*8}=\frac{380-4\sqrt{985}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+4\sqrt{985}}{2*8}=\frac{380+4\sqrt{985}}{16}
$