4x2+42x=343

Solution for 4x2+42x=343 equation:

4x^2+42x=343

We move all terms to the left:

4x^2+42x-(343)=0

a = 4; b = 42; c = -343;
Δ = b2-4ac
Δ = 422-4·4·(-343)
Δ = 7252
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:

$\sqrt{\Delta}=\sqrt{7252}=\sqrt{196*37}=\sqrt{196}*\sqrt{37}=14\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14\sqrt{37}}{2*4}=\frac{-42-14\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14\sqrt{37}}{2*4}=\frac{-42+14\sqrt{37}}{8}
$