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x*x-3x-5x+15=5x*x
We move all terms to the left:
x*x-3x-5x+15-(5x*x)=0
We add all the numbers together, and all the variables
x*x-3x-5x-(+5x*x)+15=0
We add all the numbers together, and all the variables
-8x+x*x-(+5x*x)+15=0
Wy multiply elements
x^2-8x-(+5x*x)+15=0
We get rid of parentheses
x^2-8x-5x*x+15=0
Wy multiply elements
x^2-5x^2-8x+15=0
We add all the numbers together, and all the variables
-4x^2-8x+15=0
a = -4; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·(-4)·15
Δ = 304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*-4}=\frac{8-4\sqrt{19}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*-4}=\frac{8+4\sqrt{19}}{-8} $
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