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10x^2-4x-15=6
We move all terms to the left:
10x^2-4x-15-(6)=0
We add all the numbers together, and all the variables
10x^2-4x-21=0
a = 10; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·10·(-21)
Δ = 856
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{214}}{2*10}=\frac{4-2\sqrt{214}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{214}}{2*10}=\frac{4+2\sqrt{214}}{20} $
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