0,2y+2,3=7/10y-3,2

Solution for 0,2y+2,3=7/10y-3,2 equation:

0.2y+2.3=7/10y-3.2

We move all terms to the left:

0.2y+2.3-(7/10y-3.2)=0


Domain of the equation: 10y-3.2)!=0

y∈R


We get rid of parentheses

0.2y-7/10y+3.2+2.3=0

We multiply all the terms by the denominator


(0.2y)*10y+(3.2)*10y+(2.3)*10y-7=0

We add all the numbers together, and all the variables

(+0.2y)*10y+(3.2)*10y+(2.3)*10y-7=0

We multiply parentheses

0y^2+32y+23y-7=0

We add all the numbers together, and all the variables

y^2+55y-7=0

a = 1; b = 55; c = -7;
Δ = b2-4ac
Δ = 552-4·1·(-7)
Δ = 3053
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{3053}}{2*1}=\frac{-55-\sqrt{3053}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3053}}{2*1}=\frac{-55+\sqrt{3053}}{2}
$