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

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

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

We move all terms to the left:

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


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

-5(x-3)x

We multiply parentheses

-5x^2+15x

Back to the equation:

-(-5x^2+15x)


We get rid of parentheses

5x^2-15x+3x+7=0

We add all the numbers together, and all the variables

5x^2-12x+7=0

a = 5; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·5·7
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*5}=\frac{14}{10}
=1+2/5
$