8x^2+78x+12=0

Solution for 8x^2+78x+12=0 equation:

8x^2+78x+12=0

a = 8; b = 78; c = +12;
Δ = b2-4ac
Δ = 782-4·8·12
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-10\sqrt{57}}{2*8}=\frac{-78-10\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+10\sqrt{57}}{2*8}=\frac{-78+10\sqrt{57}}{16}
$