t*t+8t-29=0

Solution for t*t+8t-29=0 equation:

t*t+8t-29=0

We add all the numbers together, and all the variables

8t+t*t-29=0

Wy multiply elements

t^2+8t-29=0

a = 1; b = 8; c = -29;
Δ = b2-4ac
Δ = 82-4·1·(-29)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{5}}{2*1}=\frac{-8-6\sqrt{5}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{5}}{2*1}=\frac{-8+6\sqrt{5}}{2}
$