6x2+8x+4=170

Solution for 6x2+8x+4=170 equation:

6x^2+8x+4=170

We move all terms to the left:

6x^2+8x+4-(170)=0

We add all the numbers together, and all the variables

6x^2+8x-166=0

a = 6; b = 8; c = -166;
Δ = b2-4ac
Δ = 82-4·6·(-166)
Δ = 4048
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:

$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{253}}{2*6}=\frac{-8-4\sqrt{253}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{253}}{2*6}=\frac{-8+4\sqrt{253}}{12}
$