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3=10x^2-7x-12
We move all terms to the left:
3-(10x^2-7x-12)=0
We get rid of parentheses
-10x^2+7x+12+3=0
We add all the numbers together, and all the variables
-10x^2+7x+15=0
a = -10; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-10)·15
Δ = 649
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{-(7)-\sqrt{649}}{2*-10}=\frac{-7-\sqrt{649}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{649}}{2*-10}=\frac{-7+\sqrt{649}}{-20} $
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