52=4x(2x+7)

Solution for 52=4x(2x+7) equation:

52=4x(2x+7)

We move all terms to the left:

52-(4x(2x+7))=0


We calculate terms in parentheses: -(4x(2x+7)), so:

4x(2x+7)

We multiply parentheses

8x^2+28x

Back to the equation:

-(8x^2+28x)


We get rid of parentheses

-8x^2-28x+52=0

a = -8; b = -28; c = +52;
Δ = b2-4ac
Δ = -282-4·(-8)·52
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12\sqrt{17}}{2*-8}=\frac{28-12\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12\sqrt{17}}{2*-8}=\frac{28+12\sqrt{17}}{-16}
$