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(5x-4)(2x-3)=3
We move all terms to the left:
(5x-4)(2x-3)-(3)=0
We multiply parentheses ..
(+10x^2-15x-8x+12)-3=0
We get rid of parentheses
10x^2-15x-8x+12-3=0
We add all the numbers together, and all the variables
10x^2-23x+9=0
a = 10; b = -23; c = +9;
Δ = b2-4ac
Δ = -232-4·10·9
Δ = 169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*10}=\frac{10}{20} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*10}=\frac{36}{20} =1+4/5 $
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