75x=6x^2

Solution for 75x=6x^2 equation:

75x=6x^2

We move all terms to the left:

75x-(6x^2)=0

determiningTheFunctionDomain
-6x^2+75x=0

a = -6; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-6)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-6}=\frac{-150}{-12}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-6}=\frac{0}{-12}
=0
$