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5x(2x+3)-x+8=13
We move all terms to the left:
5x(2x+3)-x+8-(13)=0
We add all the numbers together, and all the variables
-1x+5x(2x+3)-5=0
We multiply parentheses
10x^2-1x+15x-5=0
We add all the numbers together, and all the variables
10x^2+14x-5=0
a = 10; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·10·(-5)
Δ = 396
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{11}}{2*10}=\frac{-14-6\sqrt{11}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{11}}{2*10}=\frac{-14+6\sqrt{11}}{20} $
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