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2x(5x-147)+116=360
We move all terms to the left:
2x(5x-147)+116-(360)=0
We add all the numbers together, and all the variables
2x(5x-147)-244=0
We multiply parentheses
10x^2-294x-244=0
a = 10; b = -294; c = -244;
Δ = b2-4ac
Δ = -2942-4·10·(-244)
Δ = 96196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{96196}=\sqrt{4*24049}=\sqrt{4}*\sqrt{24049}=2\sqrt{24049}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{24049}}{2*10}=\frac{294-2\sqrt{24049}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{24049}}{2*10}=\frac{294+2\sqrt{24049}}{20} $
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