2t(t-7)=3t

Solution for 2t(t-7)=3t equation:

2t(t-7)=3t

We move all terms to the left:

2t(t-7)-(3t)=0

We add all the numbers together, and all the variables

-3t+2t(t-7)=0

We multiply parentheses

2t^2-3t-14t=0

We add all the numbers together, and all the variables

2t^2-17t=0

a = 2; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·2·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*2}=\frac{0}{4}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*2}=\frac{34}{4}
=8+1/2
$