5x(2x-3)=7(3x+4)

Solution for 5x(2x-3)=7(3x+4) equation:

5x(2x-3)=7(3x+4)

We move all terms to the left:

5x(2x-3)-(7(3x+4))=0

We multiply parentheses

10x^2-15x-(7(3x+4))=0


We calculate terms in parentheses: -(7(3x+4)), so:

7(3x+4)

We multiply parentheses

21x+28

Back to the equation:

-(21x+28)


We get rid of parentheses

10x^2-15x-21x-28=0

We add all the numbers together, and all the variables

10x^2-36x-28=0

a = 10; b = -36; c = -28;
Δ = b2-4ac
Δ = -362-4·10·(-28)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{151}}{2*10}=\frac{36-4\sqrt{151}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{151}}{2*10}=\frac{36+4\sqrt{151}}{20}
$