-91=-7a(3a-1)

Solution for -91=-7a(3a-1) equation:

-91=-7a(3a-1)

We move all terms to the left:

-91-(-7a(3a-1))=0


We calculate terms in parentheses: -(-7a(3a-1)), so:

-7a(3a-1)

We multiply parentheses

-21a^2+7a

Back to the equation:

-(-21a^2+7a)


We get rid of parentheses

21a^2-7a-91=0

a = 21; b = -7; c = -91;
Δ = b2-4ac
Δ = -72-4·21·(-91)
Δ = 7693
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7693}=\sqrt{49*157}=\sqrt{49}*\sqrt{157}=7\sqrt{157}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{157}}{2*21}=\frac{7-7\sqrt{157}}{42}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{157}}{2*21}=\frac{7+7\sqrt{157}}{42}
$