(4x-30)(4x-14)=180

Solution for (4x-30)(4x-14)=180 equation:

(4x-30)(4x-14)=180

We move all terms to the left:

(4x-30)(4x-14)-(180)=0

We multiply parentheses ..

(+16x^2-56x-120x+420)-180=0

We get rid of parentheses

16x^2-56x-120x+420-180=0

We add all the numbers together, and all the variables

16x^2-176x+240=0

a = 16; b = -176; c = +240;
Δ = b2-4ac
Δ = -1762-4·16·240
Δ = 15616
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:

$\sqrt{\Delta}=\sqrt{15616}=\sqrt{256*61}=\sqrt{256}*\sqrt{61}=16\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-16\sqrt{61}}{2*16}=\frac{176-16\sqrt{61}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+16\sqrt{61}}{2*16}=\frac{176+16\sqrt{61}}{32}
$