10t(t-2)=7t-4

Solution for 10t(t-2)=7t-4 equation:

10t(t-2)=7t-4

We move all terms to the left:

10t(t-2)-(7t-4)=0

We multiply parentheses

10t^2-20t-(7t-4)=0

We get rid of parentheses

10t^2-20t-7t+4=0

We add all the numbers together, and all the variables

10t^2-27t+4=0

a = 10; b = -27; c = +4;
Δ = b2-4ac
Δ = -272-4·10·4
Δ = 569
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{-(-27)-\sqrt{569}}{2*10}=\frac{27-\sqrt{569}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{569}}{2*10}=\frac{27+\sqrt{569}}{20}
$