7/10x+3=17x

Solution for 7/10x+3=17x equation:

7/10x+3=17x

We move all terms to the left:

7/10x+3-(17x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-17x+7/10x+3=0

We multiply all the terms by the denominator


-17x*10x+3*10x+7=0

Wy multiply elements

-170x^2+30x+7=0

a = -170; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·(-170)·7
Δ = 5660
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:

$\sqrt{\Delta}=\sqrt{5660}=\sqrt{4*1415}=\sqrt{4}*\sqrt{1415}=2\sqrt{1415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{1415}}{2*-170}=\frac{-30-2\sqrt{1415}}{-340}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{1415}}{2*-170}=\frac{-30+2\sqrt{1415}}{-340}
$