5x(2x-3)-4x+9=8-x

Solution for 5x(2x-3)-4x+9=8-x equation:

5x(2x-3)-4x+9=8-x

We move all terms to the left:

5x(2x-3)-4x+9-(8-x)=0

We add all the numbers together, and all the variables

5x(2x-3)-4x-(-1x+8)+9=0

We add all the numbers together, and all the variables

-4x+5x(2x-3)-(-1x+8)+9=0

We multiply parentheses

10x^2-4x-15x-(-1x+8)+9=0

We get rid of parentheses

10x^2-4x-15x+1x-8+9=0

We add all the numbers together, and all the variables

10x^2-18x+1=0

a = 10; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·10·1
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{71}}{2*10}=\frac{18-2\sqrt{71}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{71}}{2*10}=\frac{18+2\sqrt{71}}{20}
$