x(x+24)+10=350

Solution for x(x+24)+10=350 equation:

x(x+24)+10=350

We move all terms to the left:

x(x+24)+10-(350)=0

We add all the numbers together, and all the variables

x(x+24)-340=0

We multiply parentheses

x^2+24x-340=0

a = 1; b = 24; c = -340;
Δ = b2-4ac
Δ = 242-4·1·(-340)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-44}{2*1}=\frac{-68}{2}
=-34
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+44}{2*1}=\frac{20}{2}
=10
$