6s(s-2)=5(s+10)

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

6s(s-2)=5(s+10)

We move all terms to the left:

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

We multiply parentheses

6s^2-12s-(5(s+10))=0


We calculate terms in parentheses: -(5(s+10)), so:

5(s+10)

We multiply parentheses

5s+50

Back to the equation:

-(5s+50)


We get rid of parentheses

6s^2-12s-5s-50=0

We add all the numbers together, and all the variables

6s^2-17s-50=0

a = 6; b = -17; c = -50;
Δ = b2-4ac
Δ = -172-4·6·(-50)
Δ = 1489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{1489}}{2*6}=\frac{17-\sqrt{1489}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1489}}{2*6}=\frac{17+\sqrt{1489}}{12}
$