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

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



5x(2x+7)=3x+4
We move all terms to the left:
5x(2x+7)-(3x+4)=0
We multiply parentheses
10x^2+35x-(3x+4)=0
We get rid of parentheses
10x^2+35x-3x-4=0
We add all the numbers together, and all the variables
10x^2+32x-4=0
a = 10; b = 32; c = -4;
Δ = b2-4ac
Δ = 322-4·10·(-4)
Δ = 1184
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{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{74}}{2*10}=\frac{-32-4\sqrt{74}}{20}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{74}}{2*10}=\frac{-32+4\sqrt{74}}{20}

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