7/10x+5x=19

Solution for 7/10x+5x=19 equation:

7/10x+5x=19

We move all terms to the left:

7/10x+5x-(19)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

5x+7/10x-19=0

We multiply all the terms by the denominator


5x*10x-19*10x+7=0

Wy multiply elements

50x^2-190x+7=0

a = 50; b = -190; c = +7;
Δ = b2-4ac
Δ = -1902-4·50·7
Δ = 34700
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:

$\sqrt{\Delta}=\sqrt{34700}=\sqrt{100*347}=\sqrt{100}*\sqrt{347}=10\sqrt{347}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-10\sqrt{347}}{2*50}=\frac{190-10\sqrt{347}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+10\sqrt{347}}{2*50}=\frac{190+10\sqrt{347}}{100}
$