2x(5x+3)=7x+24

Solution for 2x(5x+3)=7x+24 equation:

2x(5x+3)=7x+24

We move all terms to the left:

2x(5x+3)-(7x+24)=0

We multiply parentheses

10x^2+6x-(7x+24)=0

We get rid of parentheses

10x^2+6x-7x-24=0

We add all the numbers together, and all the variables

10x^2-1x-24=0

a = 10; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·10·(-24)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*10}=\frac{32}{20}
=1+3/5
$