8x^2+30x+21=0

Solution for 8x^2+30x+21=0 equation:

8x^2+30x+21=0

a = 8; b = 30; c = +21;
Δ = b2-4ac
Δ = 302-4·8·21
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{57}}{2*8}=\frac{-30-2\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{57}}{2*8}=\frac{-30+2\sqrt{57}}{16}
$