7x=4x^2-28

Solution for 7x=4x^2-28 equation:

7x=4x^2-28

We move all terms to the left:

7x-(4x^2-28)=0

We get rid of parentheses

-4x^2+7x+28=0

a = -4; b = 7; c = +28;
Δ = b2-4ac
Δ = 72-4·(-4)·28
Δ = 497
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{-(7)-\sqrt{497}}{2*-4}=\frac{-7-\sqrt{497}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{497}}{2*-4}=\frac{-7+\sqrt{497}}{-8}
$