3s+135=4.5(s+10)s=

Solution for 3s+135=4.5(s+10)s= equation:

3s+135=4.5(s+10)s=

We move all terms to the left:

3s+135-(4.5(s+10)s)=0


We calculate terms in parentheses: -(4.5(s+10)s), so:

4.5(s+10)s

We multiply parentheses

4s^2+40s

Back to the equation:

-(4s^2+40s)


We get rid of parentheses

-4s^2+3s-40s+135=0

We add all the numbers together, and all the variables

-4s^2-37s+135=0

a = -4; b = -37; c = +135;
Δ = b2-4ac
Δ = -372-4·(-4)·135
Δ = 3529
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{-(-37)-\sqrt{3529}}{2*-4}=\frac{37-\sqrt{3529}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{3529}}{2*-4}=\frac{37+\sqrt{3529}}{-8}
$