920=t(t-10)

Solution for 920=t(t-10) equation:

920=t(t-10)

We move all terms to the left:

920-(t(t-10))=0


We calculate terms in parentheses: -(t(t-10)), so:

t(t-10)

We multiply parentheses

t^2-10t

Back to the equation:

-(t^2-10t)


We get rid of parentheses

-t^2+10t+920=0

We add all the numbers together, and all the variables

-1t^2+10t+920=0

a = -1; b = 10; c = +920;
Δ = b2-4ac
Δ = 102-4·(-1)·920
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{105}}{2*-1}=\frac{-10-6\sqrt{105}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{105}}{2*-1}=\frac{-10+6\sqrt{105}}{-2}
$