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

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

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

We move all terms to the left:

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

We multiply parentheses

10x-(7x(2x-3))-15=0


We calculate terms in parentheses: -(7x(2x-3)), so:

7x(2x-3)

We multiply parentheses

14x^2-21x

Back to the equation:

-(14x^2-21x)


We get rid of parentheses

-14x^2+10x+21x-15=0

We add all the numbers together, and all the variables

-14x^2+31x-15=0

a = -14; b = 31; c = -15;
Δ = b2-4ac
Δ = 312-4·(-14)·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-11}{2*-14}=\frac{-42}{-28}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+11}{2*-14}=\frac{-20}{-28}
=5/7
$