42x^2+2x=8

Solution for 42x^2+2x=8 equation:

42x^2+2x=8

We move all terms to the left:

42x^2+2x-(8)=0

a = 42; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·42·(-8)
Δ = 1348
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:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{337}}{2*42}=\frac{-2-2\sqrt{337}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{337}}{2*42}=\frac{-2+2\sqrt{337}}{84}
$