7-4(9y+1)=11y(-25y+3)

Solution for 7-4(9y+1)=11y(-25y+3) equation:

7-4(9y+1)=11y(-25y+3)

We move all terms to the left:

7-4(9y+1)-(11y(-25y+3))=0

We multiply parentheses

-36y-(11y(-25y+3))-4+7=0


We calculate terms in parentheses: -(11y(-25y+3)), so:

11y(-25y+3)

We multiply parentheses

-275y^2+33y

Back to the equation:

-(-275y^2+33y)


We add all the numbers together, and all the variables

-(-275y^2+33y)-36y+3=0

We get rid of parentheses

275y^2-33y-36y+3=0

We add all the numbers together, and all the variables

275y^2-69y+3=0

a = 275; b = -69; c = +3;
Δ = b2-4ac
Δ = -692-4·275·3
Δ = 1461
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-\sqrt{1461}}{2*275}=\frac{69-\sqrt{1461}}{550}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{1461}}{2*275}=\frac{69+\sqrt{1461}}{550}
$