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10x^2-14x-5=5x-2
We move all terms to the left:
10x^2-14x-5-(5x-2)=0
We get rid of parentheses
10x^2-14x-5x+2-5=0
We add all the numbers together, and all the variables
10x^2-19x-3=0
a = 10; b = -19; c = -3;
Δ = b2-4ac
Δ = -192-4·10·(-3)
Δ = 481
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{481}}{2*10}=\frac{19-\sqrt{481}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{481}}{2*10}=\frac{19+\sqrt{481}}{20} $
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