9t-2=t+5(2t-5)/4

Solution for 9t-2=t+5(2t-5)/4 equation:

9t-2=t+5(2t-5)/4

We move all terms to the left:

9t-2-(t+5(2t-5)/4)=0

We multiply all the terms by the denominator


9t*4)-(t+5(2t-5)-2*4)=0

We add all the numbers together, and all the variables

9t*4)-(t+5(2t-5)=0

We multiply parentheses

9t*4)-(t+10t-25=0

Wy multiply elements

36t^2+10t-25=0

a = 36; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·36·(-25)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{37}}{2*36}=\frac{-10-10\sqrt{37}}{72}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{37}}{2*36}=\frac{-10+10\sqrt{37}}{72}
$