-5/6t=-15t=18

Solution for -5/6t=-15t=18 equation:

-5/6t=-15t=18

We move all terms to the left:

-5/6t-(-15t)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R


We get rid of parentheses

-5/6t+15t=0

We multiply all the terms by the denominator


15t*6t-5=0

Wy multiply elements

90t^2-5=0

a = 90; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·90·(-5)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*90}=\frac{0-30\sqrt{2}}{180}
=-\frac{30\sqrt{2}}{180}
=-\frac{\sqrt{2}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*90}=\frac{0+30\sqrt{2}}{180}
=\frac{30\sqrt{2}}{180}
=\frac{\sqrt{2}}{6}
$