21=5x^2-12x

Solution for 21=5x^2-12x equation:

21=5x^2-12x

We move all terms to the left:

21-(5x^2-12x)=0

We get rid of parentheses

-5x^2+12x+21=0

a = -5; b = 12; c = +21;
Δ = b2-4ac
Δ = 122-4·(-5)·21
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{141}}{2*-5}=\frac{-12-2\sqrt{141}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{141}}{2*-5}=\frac{-12+2\sqrt{141}}{-10}
$