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8(b-4)12b=348
We move all terms to the left:
8(b-4)12b-(348)=0
We multiply parentheses
96b^2-384b-348=0
a = 96; b = -384; c = -348;
Δ = b2-4ac
Δ = -3842-4·96·(-348)
Δ = 281088
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}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{281088}=\sqrt{2304*122}=\sqrt{2304}*\sqrt{122}=48\sqrt{122}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-48\sqrt{122}}{2*96}=\frac{384-48\sqrt{122}}{192} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+48\sqrt{122}}{2*96}=\frac{384+48\sqrt{122}}{192} $
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