4x^2+8x+7=42

Solution for 4x^2+8x+7=42 equation:

4x^2+8x+7=42

We move all terms to the left:

4x^2+8x+7-(42)=0

We add all the numbers together, and all the variables

4x^2+8x-35=0

a = 4; b = 8; c = -35;
Δ = b2-4ac
Δ = 82-4·4·(-35)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{39}}{2*4}=\frac{-8-4\sqrt{39}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{39}}{2*4}=\frac{-8+4\sqrt{39}}{8}
$