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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+12x-(-1x+5)=0

We get rid of parentheses

8x^2+12x+1x-5=0

We add all the numbers together, and all the variables

8x^2+13x-5=0

a = 8; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·8·(-5)
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{329}}{2*8}=\frac{-13-\sqrt{329}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{329}}{2*8}=\frac{-13+\sqrt{329}}{16}
$