4x(x+7)=6x+40

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Solution for 4x(x+7)=6x+40 equation:



4x(x+7)=6x+40
We move all terms to the left:
4x(x+7)-(6x+40)=0
We multiply parentheses
4x^2+28x-(6x+40)=0
We get rid of parentheses
4x^2+28x-6x-40=0
We add all the numbers together, and all the variables
4x^2+22x-40=0
a = 4; b = 22; c = -40;
Δ = b2-4ac
Δ = 222-4·4·(-40)
Δ = 1124
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:
$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{281}}{2*4}=\frac{-22-2\sqrt{281}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{281}}{2*4}=\frac{-22+2\sqrt{281}}{8} $

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