-7a(3a+10)=0

Solution for -7a(3a+10)=0 equation:

-7a(3a+10)=0

We multiply parentheses

-21a^2-70a=0

a = -21; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-21)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-21}=\frac{0}{-42}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-21}=\frac{140}{-42}
=-3+1/3
$