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11x(2x-3)=15x+2
We move all terms to the left:
11x(2x-3)-(15x+2)=0
We multiply parentheses
22x^2-33x-(15x+2)=0
We get rid of parentheses
22x^2-33x-15x-2=0
We add all the numbers together, and all the variables
22x^2-48x-2=0
a = 22; b = -48; c = -2;
Δ = b2-4ac
Δ = -482-4·22·(-2)
Δ = 2480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2480}=\sqrt{16*155}=\sqrt{16}*\sqrt{155}=4\sqrt{155}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{155}}{2*22}=\frac{48-4\sqrt{155}}{44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{155}}{2*22}=\frac{48+4\sqrt{155}}{44} $
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