75=4x^2-2x

Solution for 75=4x^2-2x equation:

75=4x^2-2x

We move all terms to the left:

75-(4x^2-2x)=0

We get rid of parentheses

-4x^2+2x+75=0

a = -4; b = 2; c = +75;
Δ = b2-4ac
Δ = 22-4·(-4)·75
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{301}}{2*-4}=\frac{-2-2\sqrt{301}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{301}}{2*-4}=\frac{-2+2\sqrt{301}}{-8}
$