(t-3)(t+5)=-7

Solution for (t-3)(t+5)=-7 equation:

(t-3)(t+5)=-7

We move all terms to the left:

(t-3)(t+5)-(-7)=0

We add all the numbers together, and all the variables

(t-3)(t+5)+7=0

We multiply parentheses ..

(+t^2+5t-3t-15)+7=0

We get rid of parentheses

t^2+5t-3t-15+7=0

We add all the numbers together, and all the variables

t^2+2t-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$