84=10x^2-4x

Solution for 84=10x^2-4x equation:

84=10x^2-4x

We move all terms to the left:

84-(10x^2-4x)=0

We get rid of parentheses

-10x^2+4x+84=0

a = -10; b = 4; c = +84;
Δ = b2-4ac
Δ = 42-4·(-10)·84
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{211}}{2*-10}=\frac{-4-4\sqrt{211}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{211}}{2*-10}=\frac{-4+4\sqrt{211}}{-20}
$