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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

5x^2+4x+15x+2x-4-5=0

We add all the numbers together, and all the variables

5x^2+21x-9=0

a = 5; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·5·(-9)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{69}}{2*5}=\frac{-21-3\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{69}}{2*5}=\frac{-21+3\sqrt{69}}{10}
$