(5t+)4t+18=42

Solution for (5t+)4t+18=42 equation:

(5t+)4t+18=42

We move all terms to the left:

(5t+)4t+18-(42)=0

We add all the numbers together, and all the variables

(+5t)4t+18-42=0

We add all the numbers together, and all the variables

(+5t)4t-24=0

We multiply parentheses

20t^2-24=0

a = 20; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·20·(-24)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*20}=\frac{0-8\sqrt{30}}{40}
=-\frac{8\sqrt{30}}{40}
=-\frac{\sqrt{30}}{5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*20}=\frac{0+8\sqrt{30}}{40}
=\frac{8\sqrt{30}}{40}
=\frac{\sqrt{30}}{5}
$