4x^2+16x=34

Solution for 4x^2+16x=34 equation:

4x^2+16x=34

We move all terms to the left:

4x^2+16x-(34)=0

a = 4; b = 16; c = -34;
Δ = b2-4ac
Δ = 162-4·4·(-34)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20\sqrt{2}}{2*4}=\frac{-16-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20\sqrt{2}}{2*4}=\frac{-16+20\sqrt{2}}{8}
$