5t^2-30t=10

Solution for 5t^2-30t=10 equation:

5t^2-30t=10

We move all terms to the left:

5t^2-30t-(10)=0

a = 5; b = -30; c = -10;
Δ = b2-4ac
Δ = -302-4·5·(-10)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{11}}{2*5}=\frac{30-10\sqrt{11}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{11}}{2*5}=\frac{30+10\sqrt{11}}{10}
$