75x^2-6x=12

Solution for 75x^2-6x=12 equation:

75x^2-6x=12

We move all terms to the left:

75x^2-6x-(12)=0

a = 75; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·75·(-12)
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{101}}{2*75}=\frac{6-6\sqrt{101}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{101}}{2*75}=\frac{6+6\sqrt{101}}{150}
$