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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

3(4x+7)

We multiply parentheses

12x+21

Back to the equation:

-(12x+21)


We get rid of parentheses

10x^2-15x-12x-21=0

We add all the numbers together, and all the variables

10x^2-27x-21=0

a = 10; b = -27; c = -21;
Δ = b2-4ac
Δ = -272-4·10·(-21)
Δ = 1569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{1569}}{2*10}=\frac{27-\sqrt{1569}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1569}}{2*10}=\frac{27+\sqrt{1569}}{20}
$