5t^2-100t=45

Solution for 5t^2-100t=45 equation:

5t^2-100t=45

We move all terms to the left:

5t^2-100t-(45)=0

a = 5; b = -100; c = -45;
Δ = b2-4ac
Δ = -1002-4·5·(-45)
Δ = 10900
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:

$\sqrt{\Delta}=\sqrt{10900}=\sqrt{100*109}=\sqrt{100}*\sqrt{109}=10\sqrt{109}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{109}}{2*5}=\frac{100-10\sqrt{109}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{109}}{2*5}=\frac{100+10\sqrt{109}}{10}
$