x=43/43x-10

Solution for x=43/43x-10 equation:

x=43/43x-10

We move all terms to the left:

x-(43/43x-10)=0


Domain of the equation: 43x-10)!=0

x∈R


We get rid of parentheses

x-43/43x+10=0

We multiply all the terms by the denominator


x*43x+10*43x-43=0

Wy multiply elements

43x^2+430x-43=0

a = 43; b = 430; c = -43;
Δ = b2-4ac
Δ = 4302-4·43·(-43)
Δ = 192296
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:

$\sqrt{\Delta}=\sqrt{192296}=\sqrt{7396*26}=\sqrt{7396}*\sqrt{26}=86\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(430)-86\sqrt{26}}{2*43}=\frac{-430-86\sqrt{26}}{86}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(430)+86\sqrt{26}}{2*43}=\frac{-430+86\sqrt{26}}{86}
$