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5x(2x+6)=8x-11
We move all terms to the left:
5x(2x+6)-(8x-11)=0
We multiply parentheses
10x^2+30x-(8x-11)=0
We get rid of parentheses
10x^2+30x-8x+11=0
We add all the numbers together, and all the variables
10x^2+22x+11=0
a = 10; b = 22; c = +11;
Δ = b2-4ac
Δ = 222-4·10·11
Δ = 44
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{11}}{2*10}=\frac{-22-2\sqrt{11}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{11}}{2*10}=\frac{-22+2\sqrt{11}}{20} $
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