5x(x+5)=6-3x

Solution for 5x(x+5)=6-3x equation:

5x(x+5)=6-3x

We move all terms to the left:

5x(x+5)-(6-3x)=0

We add all the numbers together, and all the variables

5x(x+5)-(-3x+6)=0

We multiply parentheses

5x^2+25x-(-3x+6)=0

We get rid of parentheses

5x^2+25x+3x-6=0

We add all the numbers together, and all the variables

5x^2+28x-6=0

a = 5; b = 28; c = -6;
Δ = b2-4ac
Δ = 282-4·5·(-6)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{226}}{2*5}=\frac{-28-2\sqrt{226}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{226}}{2*5}=\frac{-28+2\sqrt{226}}{10}
$