(2x-3)*(4x-1)=100

Solution for (2x-3)*(4x-1)=100 equation:

(2x-3)(4x-1)=100

We move all terms to the left:

(2x-3)(4x-1)-(100)=0

We multiply parentheses ..

(+8x^2-2x-12x+3)-100=0

We get rid of parentheses

8x^2-2x-12x+3-100=0

We add all the numbers together, and all the variables

8x^2-14x-97=0

a = 8; b = -14; c = -97;
Δ = b2-4ac
Δ = -142-4·8·(-97)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10\sqrt{33}}{2*8}=\frac{14-10\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10\sqrt{33}}{2*8}=\frac{14+10\sqrt{33}}{16}
$