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5x(2x+1)=25-3x
We move all terms to the left:
5x(2x+1)-(25-3x)=0
We add all the numbers together, and all the variables
5x(2x+1)-(-3x+25)=0
We multiply parentheses
10x^2+5x-(-3x+25)=0
We get rid of parentheses
10x^2+5x+3x-25=0
We add all the numbers together, and all the variables
10x^2+8x-25=0
a = 10; b = 8; c = -25;
Δ = b2-4ac
Δ = 82-4·10·(-25)
Δ = 1064
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{266}}{2*10}=\frac{-8-2\sqrt{266}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{266}}{2*10}=\frac{-8+2\sqrt{266}}{20} $
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