5x(2x+4)=10x-3+24

Solution for 5x(2x+4)=10x-3+24 equation:

5x(2x+4)=10x-3+24

We move all terms to the left:

5x(2x+4)-(10x-3+24)=0

We add all the numbers together, and all the variables

5x(2x+4)-(10x+21)=0

We multiply parentheses

10x^2+20x-(10x+21)=0

We get rid of parentheses

10x^2+20x-10x-21=0

We add all the numbers together, and all the variables

10x^2+10x-21=0

a = 10; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·10·(-21)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{235}}{2*10}=\frac{-10-2\sqrt{235}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{235}}{2*10}=\frac{-10+2\sqrt{235}}{20}
$