14+4x-22=-9(2-x)5x

Solution for 14+4x-22=-9(2-x)5x equation:

14+4x-22=-9(2-x)5x

We move all terms to the left:

14+4x-22-(-9(2-x)5x)=0

We add all the numbers together, and all the variables

4x-(-9(-1x+2)5x)+14-22=0

We add all the numbers together, and all the variables

4x-(-9(-1x+2)5x)-8=0


We calculate terms in parentheses: -(-9(-1x+2)5x), so:

-9(-1x+2)5x

We multiply parentheses

45x^2-90x

Back to the equation:

-(45x^2-90x)


We get rid of parentheses

-45x^2+4x+90x-8=0

We add all the numbers together, and all the variables

-45x^2+94x-8=0

a = -45; b = 94; c = -8;
Δ = b2-4ac
Δ = 942-4·(-45)·(-8)
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(94)-86}{2*-45}=\frac{-180}{-90}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(94)+86}{2*-45}=\frac{-8}{-90}
=4/45
$