5x(x+3)=4x-(1-x)

Solution for 5x(x+3)=4x-(1-x) equation:

5x(x+3)=4x-(1-x)

We move all terms to the left:

5x(x+3)-(4x-(1-x))=0

We add all the numbers together, and all the variables

5x(x+3)-(4x-(-1x+1))=0

We multiply parentheses

5x^2+15x-(4x-(-1x+1))=0


We calculate terms in parentheses: -(4x-(-1x+1)), so:

4x-(-1x+1)

We get rid of parentheses

4x+1x-1

We add all the numbers together, and all the variables

5x-1

Back to the equation:

-(5x-1)


We get rid of parentheses

5x^2+15x-5x+1=0

We add all the numbers together, and all the variables

5x^2+10x+1=0

a = 5; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·5·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*5}=\frac{-10-4\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*5}=\frac{-10+4\sqrt{5}}{10}
$