5(3x-7)(9-2x)=(15+4X)

Solution for 5(3x-7)(9-2x)=(15+4X) equation:

5(3x-7)(9-2x)=(15+4x)

We move all terms to the left:

5(3x-7)(9-2x)-((15+4x))=0

We add all the numbers together, and all the variables

5(3x-7)(-2x+9)-((4x+15))=0

We multiply parentheses ..

5(-6x^2+27x+14x-63)-((4x+15))=0


We calculate terms in parentheses: -((4x+15)), so:

(4x+15)

We get rid of parentheses

4x+15

Back to the equation:

-(4x+15)


We multiply parentheses

-30x^2+135x+70x-(4x+15)-315=0

We get rid of parentheses

-30x^2+135x+70x-4x-15-315=0

We add all the numbers together, and all the variables

-30x^2+201x-330=0

a = -30; b = 201; c = -330;
Δ = b2-4ac
Δ = 2012-4·(-30)·(-330)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(201)-3\sqrt{89}}{2*-30}=\frac{-201-3\sqrt{89}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+3\sqrt{89}}{2*-30}=\frac{-201+3\sqrt{89}}{-60}
$