6x^2+100x+30=0

Solution for 6x^2+100x+30=0 equation:

6x^2+100x+30=0

a = 6; b = 100; c = +30;
Δ = b2-4ac
Δ = 1002-4·6·30
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-8\sqrt{145}}{2*6}=\frac{-100-8\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+8\sqrt{145}}{2*6}=\frac{-100+8\sqrt{145}}{12}
$