-(5/6)(9+2t)=40

Solution for -(5/6)(9+2t)=40 equation:

-(5/6)(9+2t)=40

We move all terms to the left:

-(5/6)(9+2t)-(40)=0


Domain of the equation: 6)(9+2t)!=0

t∈R


We add all the numbers together, and all the variables

-(+5/6)(2t+9)-40=0

We multiply parentheses ..

-(+10t^2+5/6*9)-40=0

We multiply all the terms by the denominator


-(+10t^2+5-40*6*9)=0

We get rid of parentheses

-10t^2-5+40*6*9=0

We add all the numbers together, and all the variables

-10t^2+2155=0

a = -10; b = 0; c = +2155;
Δ = b2-4ac
Δ = 02-4·(-10)·2155
Δ = 86200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{86200}=\sqrt{100*862}=\sqrt{100}*\sqrt{862}=10\sqrt{862}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{862}}{2*-10}=\frac{0-10\sqrt{862}}{-20}
=-\frac{10\sqrt{862}}{-20}
=-\frac{\sqrt{862}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{862}}{2*-10}=\frac{0+10\sqrt{862}}{-20}
=\frac{10\sqrt{862}}{-20}
=\frac{\sqrt{862}}{-2}
$