X+10/2x+10=60

Solution for X+10/2x+10=60 equation:

X+10/2X+10=60

We move all terms to the left:

X+10/2X+10-(60)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+10/2X-50=0

We multiply all the terms by the denominator


X*2X-50*2X+10=0

Wy multiply elements

2X^2-100X+10=0

a = 2; b = -100; c = +10;
Δ = b2-4ac
Δ = -1002-4·2·10
Δ = 9920
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:

$\sqrt{\Delta}=\sqrt{9920}=\sqrt{64*155}=\sqrt{64}*\sqrt{155}=8\sqrt{155}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-8\sqrt{155}}{2*2}=\frac{100-8\sqrt{155}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+8\sqrt{155}}{2*2}=\frac{100+8\sqrt{155}}{4}
$