5(x+5)=3(-9x+x^2)

Solution for 5(x+5)=3(-9x+x^2) equation:

5(x+5)=3(-9x+x^2)

We move all terms to the left:

5(x+5)-(3(-9x+x^2))=0

We multiply parentheses

-(3(-9x+x^2))+5x+25=0


We calculate terms in parentheses: -(3(-9x+x^2)), so:

3(-9x+x^2)

We multiply parentheses

3x^2-27x

Back to the equation:

-(3x^2-27x)


We add all the numbers together, and all the variables

5x-(3x^2-27x)+25=0

We get rid of parentheses

-3x^2+5x+27x+25=0

We add all the numbers together, and all the variables

-3x^2+32x+25=0

a = -3; b = 32; c = +25;
Δ = b2-4ac
Δ = 322-4·(-3)·25
Δ = 1324
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:

$\sqrt{\Delta}=\sqrt{1324}=\sqrt{4*331}=\sqrt{4}*\sqrt{331}=2\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{331}}{2*-3}=\frac{-32-2\sqrt{331}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{331}}{2*-3}=\frac{-32+2\sqrt{331}}{-6}
$