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5x^2-20x-370=-15
We move all terms to the left:
5x^2-20x-370-(-15)=0
We add all the numbers together, and all the variables
5x^2-20x-355=0
a = 5; b = -20; c = -355;
Δ = b2-4ac
Δ = -202-4·5·(-355)
Δ = 7500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7500}=\sqrt{2500*3}=\sqrt{2500}*\sqrt{3}=50\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-50\sqrt{3}}{2*5}=\frac{20-50\sqrt{3}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+50\sqrt{3}}{2*5}=\frac{20+50\sqrt{3}}{10} $
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