-s(s+4)=6(s-10)

Solution for -s(s+4)=6(s-10) equation:

-s(s+4)=6(s-10)

We move all terms to the left:

-s(s+4)-(6(s-10))=0

We multiply parentheses

-s^2-4s-(6(s-10))=0


We calculate terms in parentheses: -(6(s-10)), so:

6(s-10)

We multiply parentheses

6s-60

Back to the equation:

-(6s-60)


We add all the numbers together, and all the variables

-1s^2-4s-(6s-60)=0

We get rid of parentheses

-1s^2-4s-6s+60=0

We add all the numbers together, and all the variables

-1s^2-10s+60=0

a = -1; b = -10; c = +60;
Δ = b2-4ac
Δ = -102-4·(-1)·60
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*-1}=\frac{10-2\sqrt{85}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*-1}=\frac{10+2\sqrt{85}}{-2}
$