t^2+10t-175=0

Solution for t^2+10t-175=0 equation:

t^2+10t-175=0

a = 1; b = 10; c = -175;
Δ = b2-4ac
Δ = 102-4·1·(-175)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20\sqrt{2}}{2*1}=\frac{-10-20\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20\sqrt{2}}{2*1}=\frac{-10+20\sqrt{2}}{2}
$