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(7y+27)(15y-5)=125
We move all terms to the left:
(7y+27)(15y-5)-(125)=0
We multiply parentheses ..
(+105y^2-35y+405y-135)-125=0
We get rid of parentheses
105y^2-35y+405y-135-125=0
We add all the numbers together, and all the variables
105y^2+370y-260=0
a = 105; b = 370; c = -260;
Δ = b2-4ac
Δ = 3702-4·105·(-260)
Δ = 246100
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{246100}=\sqrt{100*2461}=\sqrt{100}*\sqrt{2461}=10\sqrt{2461}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(370)-10\sqrt{2461}}{2*105}=\frac{-370-10\sqrt{2461}}{210} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(370)+10\sqrt{2461}}{2*105}=\frac{-370+10\sqrt{2461}}{210} $
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