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12-x(x+15)=-348
We move all terms to the left:
12-x(x+15)-(-348)=0
We add all the numbers together, and all the variables
-x(x+15)+360=0
We multiply parentheses
-x^2-15x+360=0
We add all the numbers together, and all the variables
-1x^2-15x+360=0
a = -1; b = -15; c = +360;
Δ = b2-4ac
Δ = -152-4·(-1)·360
Δ = 1665
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{185}}{2*-1}=\frac{15-3\sqrt{185}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{185}}{2*-1}=\frac{15+3\sqrt{185}}{-2} $
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