x^2-45x+296=0

Solution for x^2-45x+296=0 equation:

x^2-45x+296=0

a = 1; b = -45; c = +296;
Δ = b2-4ac
Δ = -452-4·1·296
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-29}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+29}{2*1}=\frac{74}{2}
=37
$