-7x(-5-x)=-9(2x-1)-1

Solution for -7x(-5-x)=-9(2x-1)-1 equation:

-7x(-5-x)=-9(2x-1)-1

We move all terms to the left:

-7x(-5-x)-(-9(2x-1)-1)=0

We add all the numbers together, and all the variables

-7x(-1x-5)-(-9(2x-1)-1)=0

We multiply parentheses

7x^2+35x-(-9(2x-1)-1)=0


We calculate terms in parentheses: -(-9(2x-1)-1), so:

-9(2x-1)-1

We multiply parentheses

-18x+9-1

We add all the numbers together, and all the variables

-18x+8

Back to the equation:

-(-18x+8)


We get rid of parentheses

7x^2+35x+18x-8=0

We add all the numbers together, and all the variables

7x^2+53x-8=0

a = 7; b = 53; c = -8;
Δ = b2-4ac
Δ = 532-4·7·(-8)
Δ = 3033
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-3\sqrt{337}}{2*7}=\frac{-53-3\sqrt{337}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+3\sqrt{337}}{2*7}=\frac{-53+3\sqrt{337}}{14}
$