72x-30/6x-700-(700-x)=0

Solution for 72x-30/6x-700-(700-x)=0 equation:

72x-30/6x-700-(700-x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

72x-30/6x-(-1x+700)-700=0

We get rid of parentheses

72x-30/6x+1x-700-700=0

We multiply all the terms by the denominator


72x*6x+1x*6x-700*6x-700*6x-30=0

Wy multiply elements

432x^2+6x^2-4200x-4200x-30=0

We add all the numbers together, and all the variables

438x^2-8400x-30=0

a = 438; b = -8400; c = -30;
Δ = b2-4ac
Δ = -84002-4·438·(-30)
Δ = 70612560
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:

$\sqrt{\Delta}=\sqrt{70612560}=\sqrt{1296*54485}=\sqrt{1296}*\sqrt{54485}=36\sqrt{54485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8400)-36\sqrt{54485}}{2*438}=\frac{8400-36\sqrt{54485}}{876}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8400)+36\sqrt{54485}}{2*438}=\frac{8400+36\sqrt{54485}}{876}
$