# 4x(2x-3)=5x+7

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## Solution for 4x(2x-3)=5x+7 equation:

4x(2x-3)=5x+7
We move all terms to the left:
4x(2x-3)-(5x+7)=0
We multiply parentheses
8x^2-12x-(5x+7)=0
We get rid of parentheses
8x^2-12x-5x-7=0
We add all the numbers together, and all the variables
8x^2-17x-7=0
a = 8; b = -17; c = -7;Δ = b2-4acΔ = -172-4·8·(-7)Δ = 513The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{57}}{2*8}=\frac{17-3\sqrt{57}}{16}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{57}}{2*8}=\frac{17+3\sqrt{57}}{16}$

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