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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(-5a(a-6)), so:

-5a(a-6)

We multiply parentheses

-5a^2+30a

Back to the equation:

-(-5a^2+30a)


We get rid of parentheses

5a^2-30a+7a+6=0

We add all the numbers together, and all the variables

5a^2-23a+6=0

a = 5; b = -23; c = +6;
Δ = b2-4ac
Δ = -232-4·5·6
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{409}}{2*5}=\frac{23-\sqrt{409}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{409}}{2*5}=\frac{23+\sqrt{409}}{10}
$