10t(t-4)+8t=6(3t+5)-9

Solution for 10t(t-4)+8t=6(3t+5)-9 equation:

10t(t-4)+8t=6(3t+5)-9

We move all terms to the left:

10t(t-4)+8t-(6(3t+5)-9)=0

We add all the numbers together, and all the variables

8t+10t(t-4)-(6(3t+5)-9)=0

We multiply parentheses

10t^2+8t-40t-(6(3t+5)-9)=0


We calculate terms in parentheses: -(6(3t+5)-9), so:

6(3t+5)-9

We multiply parentheses

18t+30-9

We add all the numbers together, and all the variables

18t+21

Back to the equation:

-(18t+21)


We add all the numbers together, and all the variables

10t^2-32t-(18t+21)=0

We get rid of parentheses

10t^2-32t-18t-21=0

We add all the numbers together, and all the variables

10t^2-50t-21=0

a = 10; b = -50; c = -21;
Δ = b2-4ac
Δ = -502-4·10·(-21)
Δ = 3340
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:

$\sqrt{\Delta}=\sqrt{3340}=\sqrt{4*835}=\sqrt{4}*\sqrt{835}=2\sqrt{835}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{835}}{2*10}=\frac{50-2\sqrt{835}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{835}}{2*10}=\frac{50+2\sqrt{835}}{20}
$