-5x(x-7)=2(2x+3)+x+7

Solution for -5x(x-7)=2(2x+3)+x+7 equation:

-5x(x-7)=2(2x+3)+x+7

We move all terms to the left:

-5x(x-7)-(2(2x+3)+x+7)=0

We multiply parentheses

-5x^2+35x-(2(2x+3)+x+7)=0


We calculate terms in parentheses: -(2(2x+3)+x+7), so:

2(2x+3)+x+7

We add all the numbers together, and all the variables

x+2(2x+3)+7

We multiply parentheses

x+4x+6+7

We add all the numbers together, and all the variables

5x+13

Back to the equation:

-(5x+13)


We get rid of parentheses

-5x^2+35x-5x-13=0

We add all the numbers together, and all the variables

-5x^2+30x-13=0

a = -5; b = 30; c = -13;
Δ = b2-4ac
Δ = 302-4·(-5)·(-13)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-8\sqrt{10}}{2*-5}=\frac{-30-8\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{10}}{2*-5}=\frac{-30+8\sqrt{10}}{-10}
$