4x2-7x+19=9x+4

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Solution for 4x2-7x+19=9x+4 equation:



4x^2-7x+19=9x+4
We move all terms to the left:
4x^2-7x+19-(9x+4)=0
We get rid of parentheses
4x^2-7x-9x-4+19=0
We add all the numbers together, and all the variables
4x^2-16x+15=0
a = 4; b = -16; c = +15;
Δ = b2-4ac
Δ = -162-4·4·15
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*4}=\frac{12}{8} =1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*4}=\frac{20}{8} =2+1/2 $

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