(3x)(x-7)=(4x-7)

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

(3x)(x-7)=(4x-7)

We move all terms to the left:

(3x)(x-7)-((4x-7))=0

We multiply parentheses

3x^2-21x-((4x-7))=0


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

(4x-7)

We get rid of parentheses

4x-7

Back to the equation:

-(4x-7)


We get rid of parentheses

3x^2-21x-4x+7=0

We add all the numbers together, and all the variables

3x^2-25x+7=0

a = 3; b = -25; c = +7;
Δ = b2-4ac
Δ = -252-4·3·7
Δ = 541
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{-(-25)-\sqrt{541}}{2*3}=\frac{25-\sqrt{541}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{541}}{2*3}=\frac{25+\sqrt{541}}{6}
$