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

Solution for 7(x+3)+9=5(x-2)3x equation:

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

We move all terms to the left:

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

We multiply parentheses

7x-(5(x-2)3x)+21+9=0


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

5(x-2)3x

We multiply parentheses

15x^2-30x

Back to the equation:

-(15x^2-30x)


We add all the numbers together, and all the variables

7x-(15x^2-30x)+30=0

We get rid of parentheses

-15x^2+7x+30x+30=0

We add all the numbers together, and all the variables

-15x^2+37x+30=0

a = -15; b = 37; c = +30;
Δ = b2-4ac
Δ = 372-4·(-15)·30
Δ = 3169
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{-(37)-\sqrt{3169}}{2*-15}=\frac{-37-\sqrt{3169}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{3169}}{2*-15}=\frac{-37+\sqrt{3169}}{-30}
$