4/7x=3x-51

Solution for 4/7x=3x-51 equation:

4/7x=3x-51

We move all terms to the left:

4/7x-(3x-51)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

4/7x-3x+51=0

We multiply all the terms by the denominator


-3x*7x+51*7x+4=0

Wy multiply elements

-21x^2+357x+4=0

a = -21; b = 357; c = +4;
Δ = b2-4ac
Δ = 3572-4·(-21)·4
Δ = 127785
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{-(357)-\sqrt{127785}}{2*-21}=\frac{-357-\sqrt{127785}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(357)+\sqrt{127785}}{2*-21}=\frac{-357+\sqrt{127785}}{-42}
$