8x^2+6x=42

Solution for 8x^2+6x=42 equation:

8x^2+6x=42

We move all terms to the left:

8x^2+6x-(42)=0

a = 8; b = 6; c = -42;
Δ = b2-4ac
Δ = 62-4·8·(-42)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{345}}{2*8}=\frac{-6-2\sqrt{345}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{345}}{2*8}=\frac{-6+2\sqrt{345}}{16}
$