(-5-t)(7-t)=-12

Solution for (-5-t)(7-t)=-12 equation:

(-5-t)(7-t)=-12

We move all terms to the left:

(-5-t)(7-t)-(-12)=0

We add all the numbers together, and all the variables

(-1t-5)(-1t+7)-(-12)=0

We add all the numbers together, and all the variables

(-1t-5)(-1t+7)+12=0

We multiply parentheses ..

(+t^2-7t+5t-35)+12=0

We get rid of parentheses

t^2-7t+5t-35+12=0

We add all the numbers together, and all the variables

t^2-2t-23=0

a = 1; b = -2; c = -23;
Δ = b2-4ac
Δ = -22-4·1·(-23)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{6}}{2*1}=\frac{2-4\sqrt{6}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{6}}{2*1}=\frac{2+4\sqrt{6}}{2}
$