b2+10b=75

Solution for b2+10b=75 equation:

b2+10b=75

We move all terms to the left:

b2+10b-(75)=0

We add all the numbers together, and all the variables

b^2+10b-75=0

a = 1; b = 10; c = -75;
Δ = b2-4ac
Δ = 102-4·1·(-75)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*1}=\frac{-30}{2}
=-15
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*1}=\frac{10}{2}
=5
$