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(7y+6)4y=116
We move all terms to the left:
(7y+6)4y-(116)=0
We multiply parentheses
28y^2+24y-116=0
a = 28; b = 24; c = -116;
Δ = b2-4ac
Δ = 242-4·28·(-116)
Δ = 13568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13568}=\sqrt{256*53}=\sqrt{256}*\sqrt{53}=16\sqrt{53}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{53}}{2*28}=\frac{-24-16\sqrt{53}}{56} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{53}}{2*28}=\frac{-24+16\sqrt{53}}{56} $
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