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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x(-1x+2)+7x-(-3(x+5))=0

We add all the numbers together, and all the variables

7x+5x(-1x+2)-(-3(x+5))=0

We multiply parentheses

-5x^2+7x+10x-(-3(x+5))=0


We calculate terms in parentheses: -(-3(x+5)), so:

-3(x+5)

We multiply parentheses

-3x-15

Back to the equation:

-(-3x-15)


We add all the numbers together, and all the variables

-5x^2+17x-(-3x-15)=0

We get rid of parentheses

-5x^2+17x+3x+15=0

We add all the numbers together, and all the variables

-5x^2+20x+15=0

a = -5; b = 20; c = +15;
Δ = b2-4ac
Δ = 202-4·(-5)·15
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{7}}{2*-5}=\frac{-20-10\sqrt{7}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{7}}{2*-5}=\frac{-20+10\sqrt{7}}{-10}
$