6(x^2+12x+35)=0

Solution for 6(x^2+12x+35)=0 equation:

6(x^2+12x+35)=0

We multiply parentheses

6x^2+72x+210=0

a = 6; b = 72; c = +210;
Δ = b2-4ac
Δ = 722-4·6·210
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12}{2*6}=\frac{-60}{12}
=-5
$