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(8y+1)(6y+5)=90
We move all terms to the left:
(8y+1)(6y+5)-(90)=0
We multiply parentheses ..
(+48y^2+40y+6y+5)-90=0
We get rid of parentheses
48y^2+40y+6y+5-90=0
We add all the numbers together, and all the variables
48y^2+46y-85=0
a = 48; b = 46; c = -85;
Δ = b2-4ac
Δ = 462-4·48·(-85)
Δ = 18436
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18436}=\sqrt{4*4609}=\sqrt{4}*\sqrt{4609}=2\sqrt{4609}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{4609}}{2*48}=\frac{-46-2\sqrt{4609}}{96} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{4609}}{2*48}=\frac{-46+2\sqrt{4609}}{96} $
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