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5x-6*2x+3=10x^2-3x-5
We move all terms to the left:
5x-6*2x+3-(10x^2-3x-5)=0
Wy multiply elements
5x-12x-(10x^2-3x-5)+3=0
We get rid of parentheses
-10x^2+5x-12x+3x+5+3=0
We add all the numbers together, and all the variables
-10x^2-4x+8=0
a = -10; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-10)·8
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*-10}=\frac{4-4\sqrt{21}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*-10}=\frac{4+4\sqrt{21}}{-20} $
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