4x^2+28x=464

Solution for 4x^2+28x=464 equation:

4x^2+28x=464

We move all terms to the left:

4x^2+28x-(464)=0

a = 4; b = 28; c = -464;
Δ = b2-4ac
Δ = 282-4·4·(-464)
Δ = 8208
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:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{57}}{2*4}=\frac{-28-12\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{57}}{2*4}=\frac{-28+12\sqrt{57}}{8}
$