(4t-5t^2)+17(6t+2)=106t

Solution for (4t-5t^2)+17(6t+2)=106t equation:

(4t-5t^2)+17(6t+2)=106t

We move all terms to the left:

(4t-5t^2)+17(6t+2)-(106t)=0

We add all the numbers together, and all the variables

(4t-5t^2)-106t+17(6t+2)=0

We multiply parentheses

(4t-5t^2)-106t+102t+34=0

We get rid of parentheses

-5t^2+4t-106t+102t+34=0

We add all the numbers together, and all the variables

-5t^2+34=0

a = -5; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-5)·34
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{170}}{2*-5}=\frac{0-2\sqrt{170}}{-10}
=-\frac{2\sqrt{170}}{-10}
=-\frac{\sqrt{170}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{170}}{2*-5}=\frac{0+2\sqrt{170}}{-10}
=\frac{2\sqrt{170}}{-10}
=\frac{\sqrt{170}}{-5}
$