37=5x^2-2x

Solution for 37=5x^2-2x equation:

37=5x^2-2x

We move all terms to the left:

37-(5x^2-2x)=0

We get rid of parentheses

-5x^2+2x+37=0

a = -5; b = 2; c = +37;
Δ = b2-4ac
Δ = 22-4·(-5)·37
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{186}}{2*-5}=\frac{-2-2\sqrt{186}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{186}}{2*-5}=\frac{-2+2\sqrt{186}}{-10}
$