a(5a-7)=6

Solution for a(5a-7)=6 equation:

a(5a-7)=6

We move all terms to the left:

a(5a-7)-(6)=0

We multiply parentheses

5a^2-7a-6=0

a = 5; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·5·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*5}=\frac{-6}{10}
=-3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*5}=\frac{20}{10}
=2
$