7=5x^2-2x

Solution for 7=5x^2-2x equation:

7=5x^2-2x

We move all terms to the left:

7-(5x^2-2x)=0

We get rid of parentheses

-5x^2+2x+7=0

a = -5; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-5)·7
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*-5}=\frac{10}{-10}
=-1
$