x+19/100*x=7

Solution for x+19/100*x=7 equation:

x+19/100x=7

We move all terms to the left:

x+19/100x-(7)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-7*100x+19=0

Wy multiply elements

100x^2-700x+19=0

a = 100; b = -700; c = +19;
Δ = b2-4ac
Δ = -7002-4·100·19
Δ = 482400
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:

$\sqrt{\Delta}=\sqrt{482400}=\sqrt{3600*134}=\sqrt{3600}*\sqrt{134}=60\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-60\sqrt{134}}{2*100}=\frac{700-60\sqrt{134}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+60\sqrt{134}}{2*100}=\frac{700+60\sqrt{134}}{200}
$