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-8b(5b-10)+5=-115
We move all terms to the left:
-8b(5b-10)+5-(-115)=0
We add all the numbers together, and all the variables
-8b(5b-10)+120=0
We multiply parentheses
-40b^2+80b+120=0
a = -40; b = 80; c = +120;
Δ = b2-4ac
Δ = 802-4·(-40)·120
Δ = 25600
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{25600}=160$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-160}{2*-40}=\frac{-240}{-80} =+3 $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+160}{2*-40}=\frac{80}{-80} =-1 $
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