6a(2a+10)=5(a+5)

Solution for 6a(2a+10)=5(a+5) equation:

6a(2a+10)=5(a+5)

We move all terms to the left:

6a(2a+10)-(5(a+5))=0

We multiply parentheses

12a^2+60a-(5(a+5))=0


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

5(a+5)

We multiply parentheses

5a+25

Back to the equation:

-(5a+25)


We get rid of parentheses

12a^2+60a-5a-25=0

We add all the numbers together, and all the variables

12a^2+55a-25=0

a = 12; b = 55; c = -25;
Δ = b2-4ac
Δ = 552-4·12·(-25)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-65}{2*12}=\frac{-120}{24}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+65}{2*12}=\frac{10}{24}
=5/12
$