-2t(5t-3)+3t=2t-7

Solution for -2t(5t-3)+3t=2t-7 equation:

-2t(5t-3)+3t=2t-7

We move all terms to the left:

-2t(5t-3)+3t-(2t-7)=0

We add all the numbers together, and all the variables

3t-2t(5t-3)-(2t-7)=0

We multiply parentheses

-10t^2+3t+6t-(2t-7)=0

We get rid of parentheses

-10t^2+3t+6t-2t+7=0

We add all the numbers together, and all the variables

-10t^2+7t+7=0

a = -10; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·(-10)·7
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{329}}{2*-10}=\frac{-7-\sqrt{329}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{329}}{2*-10}=\frac{-7+\sqrt{329}}{-20}
$