x^2=3x+92

Solution for x^2=3x+92 equation:

x^2=3x+92

We move all terms to the left:

x^2-(3x+92)=0

We get rid of parentheses

x^2-3x-92=0

a = 1; b = -3; c = -92;
Δ = b2-4ac
Δ = -32-4·1·(-92)
Δ = 377
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)-\sqrt{377}}{2*1}=\frac{3-\sqrt{377}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{377}}{2*1}=\frac{3+\sqrt{377}}{2}
$