3x*x+5x=42x

Solution for 3x*x+5x=42x equation:

3x*x+5x=42x

We move all terms to the left:

3x*x+5x-(42x)=0

We add all the numbers together, and all the variables

-37x+3x*x=0

Wy multiply elements

3x^2-37x=0

a = 3; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·3·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*3}=\frac{74}{6}
=12+1/3
$