5x(-1)=5x^2-(8-3x)

Solution for 5x(-1)=5x^2-(8-3x) equation:

5x(-1)=5x^2-(8-3x)

We move all terms to the left:

5x(-1)-(5x^2-(8-3x))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x-(5x^2-(-3x+8))=0


We calculate terms in parentheses: -(5x^2-(-3x+8)), so:

5x^2-(-3x+8)

We get rid of parentheses

5x^2+3x-8

Back to the equation:

-(5x^2+3x-8)


We get rid of parentheses

-5x^2-5x-3x+8=0

We add all the numbers together, and all the variables

-5x^2-8x+8=0

a = -5; b = -8; c = +8;
Δ = b2-4ac
Δ = -82-4·(-5)·8
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{14}}{2*-5}=\frac{8-4\sqrt{14}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{14}}{2*-5}=\frac{8+4\sqrt{14}}{-10}
$