52=7x^2-47x

Solution for 52=7x^2-47x equation:

52=7x^2-47x

We move all terms to the left:

52-(7x^2-47x)=0

We get rid of parentheses

-7x^2+47x+52=0

a = -7; b = 47; c = +52;
Δ = b2-4ac
Δ = 472-4·(-7)·52
Δ = 3665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-\sqrt{3665}}{2*-7}=\frac{-47-\sqrt{3665}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{3665}}{2*-7}=\frac{-47+\sqrt{3665}}{-14}
$