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10x-1=-4x^2
We move all terms to the left:
10x-1-(-4x^2)=0
We get rid of parentheses
4x^2+10x-1=0
a = 4; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·4·(-1)
Δ = 116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{29}}{2*4}=\frac{-10-2\sqrt{29}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{29}}{2*4}=\frac{-10+2\sqrt{29}}{8} $
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