5x-14=-4/10x+5

Solution for 5x-14=-4/10x+5 equation:

5x-14=-4/10x+5

We move all terms to the left:

5x-14-(-4/10x+5)=0


Domain of the equation: 10x+5)!=0

x∈R


We get rid of parentheses

5x+4/10x-5-14=0

We multiply all the terms by the denominator


5x*10x-5*10x-14*10x+4=0

Wy multiply elements

50x^2-50x-140x+4=0

We add all the numbers together, and all the variables

50x^2-190x+4=0

a = 50; b = -190; c = +4;
Δ = b2-4ac
Δ = -1902-4·50·4
Δ = 35300
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:

$\sqrt{\Delta}=\sqrt{35300}=\sqrt{100*353}=\sqrt{100}*\sqrt{353}=10\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-10\sqrt{353}}{2*50}=\frac{190-10\sqrt{353}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+10\sqrt{353}}{2*50}=\frac{190+10\sqrt{353}}{100}
$