9x-25=7(x+2)(5-3x)

Solution for 9x-25=7(x+2)(5-3x) equation:

9x-25=7(x+2)(5-3x)

We move all terms to the left:

9x-25-(7(x+2)(5-3x))=0

We add all the numbers together, and all the variables

9x-(7(x+2)(-3x+5))-25=0

We multiply parentheses ..

-(7(-3x^2+5x-6x+10))+9x-25=0


We calculate terms in parentheses: -(7(-3x^2+5x-6x+10)), so:

7(-3x^2+5x-6x+10)

We multiply parentheses

-21x^2+35x-42x+70

We add all the numbers together, and all the variables

-21x^2-7x+70

Back to the equation:

-(-21x^2-7x+70)


We get rid of parentheses

21x^2+7x+9x-70-25=0

We add all the numbers together, and all the variables

21x^2+16x-95=0

a = 21; b = 16; c = -95;
Δ = b2-4ac
Δ = 162-4·21·(-95)
Δ = 8236
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:

$\sqrt{\Delta}=\sqrt{8236}=\sqrt{4*2059}=\sqrt{4}*\sqrt{2059}=2\sqrt{2059}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{2059}}{2*21}=\frac{-16-2\sqrt{2059}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{2059}}{2*21}=\frac{-16+2\sqrt{2059}}{42}
$