Y=(5x+7)(2x+10)

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Solution for Y=(5x+7)(2x+10) equation:



=(5Y+7)(2Y+10)
We move all terms to the left:
-((5Y+7)(2Y+10))=0
We multiply parentheses ..
-((+10Y^2+50Y+14Y+70))=0
We calculate terms in parentheses: -((+10Y^2+50Y+14Y+70)), so:
(+10Y^2+50Y+14Y+70)
We get rid of parentheses
10Y^2+50Y+14Y+70
We add all the numbers together, and all the variables
10Y^2+64Y+70
Back to the equation:
-(10Y^2+64Y+70)
We get rid of parentheses
-10Y^2-64Y-70=0
a = -10; b = -64; c = -70;
Δ = b2-4ac
Δ = -642-4·(-10)·(-70)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-36}{2*-10}=\frac{28}{-20} =-1+2/5 $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+36}{2*-10}=\frac{100}{-20} =-5 $

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