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5x(2x-3)=7x+15
We move all terms to the left:
5x(2x-3)-(7x+15)=0
We multiply parentheses
10x^2-15x-(7x+15)=0
We get rid of parentheses
10x^2-15x-7x-15=0
We add all the numbers together, and all the variables
10x^2-22x-15=0
a = 10; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·10·(-15)
Δ = 1084
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{271}}{2*10}=\frac{22-2\sqrt{271}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{271}}{2*10}=\frac{22+2\sqrt{271}}{20} $
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