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

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
$