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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x+5x-(3x(-1x+5)+2(x+2))-15=0


We calculate terms in parentheses: -(3x(-1x+5)+2(x+2)), so:

3x(-1x+5)+2(x+2)

We multiply parentheses

-3x^2+15x+2x+4

We add all the numbers together, and all the variables

-3x^2+17x+4

Back to the equation:

-(-3x^2+17x+4)


We add all the numbers together, and all the variables

-(-3x^2+17x+4)+6x-15=0

We get rid of parentheses

3x^2-17x+6x-4-15=0

We add all the numbers together, and all the variables

3x^2-11x-19=0

a = 3; b = -11; c = -19;
Δ = b2-4ac
Δ = -112-4·3·(-19)
Δ = 349
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{349}}{2*3}=\frac{11-\sqrt{349}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{349}}{2*3}=\frac{11+\sqrt{349}}{6}
$