9(4x+2)=7(5x-8)x+

Solution for 9(4x+2)=7(5x-8)x+ equation:

9(4x+2)=7(5x-8)x+

We move all terms to the left:

9(4x+2)-(7(5x-8)x+)=0

We multiply parentheses

36x-(7(5x-8)x+)+18=0


We calculate terms in parentheses: -(7(5x-8)x+), so:

7(5x-8)x+

We add all the numbers together, and all the variables

7(5x-8)x

We multiply parentheses

35x^2-56x

Back to the equation:

-(35x^2-56x)


We get rid of parentheses

-35x^2+36x+56x+18=0

We add all the numbers together, and all the variables

-35x^2+92x+18=0

a = -35; b = 92; c = +18;
Δ = b2-4ac
Δ = 922-4·(-35)·18
Δ = 10984
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:

$\sqrt{\Delta}=\sqrt{10984}=\sqrt{4*2746}=\sqrt{4}*\sqrt{2746}=2\sqrt{2746}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-2\sqrt{2746}}{2*-35}=\frac{-92-2\sqrt{2746}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+2\sqrt{2746}}{2*-35}=\frac{-92+2\sqrt{2746}}{-70}
$