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3x+5=4x^2+x
We move all terms to the left:
3x+5-(4x^2+x)=0
We get rid of parentheses
-4x^2+3x-x+5=0
We add all the numbers together, and all the variables
-4x^2+2x+5=0
a = -4; b = 2; c = +5;
Δ = b2-4ac
Δ = 22-4·(-4)·5
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*-4}=\frac{-2-2\sqrt{21}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*-4}=\frac{-2+2\sqrt{21}}{-8} $
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