-7(a-7)(1-5a)=62

Solution for -7(a-7)(1-5a)=62 equation:

-7(a-7)(1-5a)=62

We move all terms to the left:

-7(a-7)(1-5a)-(62)=0

We add all the numbers together, and all the variables

-7(a-7)(-5a+1)-62=0

We multiply parentheses ..

-7(-5a^2+a+35a-7)-62=0

We multiply parentheses

35a^2-7a-245a+49-62=0

We add all the numbers together, and all the variables

35a^2-252a-13=0

a = 35; b = -252; c = -13;
Δ = b2-4ac
Δ = -2522-4·35·(-13)
Δ = 65324
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:

$\sqrt{\Delta}=\sqrt{65324}=\sqrt{4*16331}=\sqrt{4}*\sqrt{16331}=2\sqrt{16331}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-2\sqrt{16331}}{2*35}=\frac{252-2\sqrt{16331}}{70}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+2\sqrt{16331}}{2*35}=\frac{252+2\sqrt{16331}}{70}
$