0.7x+7=5-3/10x

Solution for 0.7x+7=5-3/10x equation:

0.7x+7=5-3/10x

We move all terms to the left:

0.7x+7-(5-3/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.7x-(-3/10x+5)+7=0

We get rid of parentheses

0.7x+3/10x-5+7=0

We multiply all the terms by the denominator


(0.7x)*10x-5*10x+7*10x+3=0

We add all the numbers together, and all the variables

(+0.7x)*10x-5*10x+7*10x+3=0

We multiply parentheses

0x^2-5*10x+7*10x+3=0

Wy multiply elements

0x^2-50x+70x+3=0

We add all the numbers together, and all the variables

x^2+20x+3=0

a = 1; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·1·3
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{97}}{2*1}=\frac{-20-2\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{97}}{2*1}=\frac{-20+2\sqrt{97}}{2}
$