0.25x+2=-25/40x-5

Solution for 0.25x+2=-25/40x-5 equation:

0.25x+2=-25/40x-5

We move all terms to the left:

0.25x+2-(-25/40x-5)=0


Domain of the equation: 40x-5)!=0

x∈R


We get rid of parentheses

0.25x+25/40x+5+2=0

We multiply all the terms by the denominator


(0.25x)*40x+5*40x+2*40x+25=0

We add all the numbers together, and all the variables

(+0.25x)*40x+5*40x+2*40x+25=0

We multiply parentheses

0x^2+5*40x+2*40x+25=0

Wy multiply elements

0x^2+200x+80x+25=0

We add all the numbers together, and all the variables

x^2+280x+25=0

a = 1; b = 280; c = +25;
Δ = b2-4ac
Δ = 2802-4·1·25
Δ = 78300
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:

$\sqrt{\Delta}=\sqrt{78300}=\sqrt{900*87}=\sqrt{900}*\sqrt{87}=30\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-30\sqrt{87}}{2*1}=\frac{-280-30\sqrt{87}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+30\sqrt{87}}{2*1}=\frac{-280+30\sqrt{87}}{2}
$