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5x^2-5x-60=290
We move all terms to the left:
5x^2-5x-60-(290)=0
We add all the numbers together, and all the variables
5x^2-5x-350=0
a = 5; b = -5; c = -350;
Δ = b2-4ac
Δ = -52-4·5·(-350)
Δ = 7025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7025}=\sqrt{25*281}=\sqrt{25}*\sqrt{281}=5\sqrt{281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{281}}{2*5}=\frac{5-5\sqrt{281}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{281}}{2*5}=\frac{5+5\sqrt{281}}{10} $
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