x^2/3.64+x=1.51

Solution for x^2/3.64+x=1.51 equation:

x^2/3.64+x=1.51

We move all terms to the left:

x^2/3.64+x-(1.51)=0

We add all the numbers together, and all the variables

x^2/3.64+x-1.51=0

We multiply all the terms by the denominator


x^2+x*3.64-(1.51)*3.64=0

We add all the numbers together, and all the variables

x^2+x*3.64-5.4964=0

Wy multiply elements

x^2+3.64x-5.4964=0

a = 1; b = 3.64; c = -5.4964;
Δ = b2-4ac
Δ = 3.642-4·1·(-5.4964)
Δ = 35.2352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3.64)-\sqrt{35.2352}}{2*1}=\frac{-3.64-\sqrt{35.2352}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.64)+\sqrt{35.2352}}{2*1}=\frac{-3.64+\sqrt{35.2352}}{2}
$