8b2-7b=+10

Solution for 8b2-7b=+10 equation:

8b^2-7b=+10

We move all terms to the left:

8b^2-7b-(+10)=0

We add all the numbers together, and all the variables

8b^2-7b-10=0

a = 8; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·8·(-10)
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{41}}{2*8}=\frac{7-3\sqrt{41}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{41}}{2*8}=\frac{7+3\sqrt{41}}{16}
$