x(2x-3)=98-3x

Solution for x(2x-3)=98-3x equation:

x(2x-3)=98-3x

We move all terms to the left:

x(2x-3)-(98-3x)=0

We add all the numbers together, and all the variables

x(2x-3)-(-3x+98)=0

We multiply parentheses

2x^2-3x-(-3x+98)=0

We get rid of parentheses

2x^2-3x+3x-98=0

We add all the numbers together, and all the variables

2x^2-98=0

a = 2; b = 0; c = -98;
Δ = b2-4ac
Δ = 02-4·2·(-98)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*2}=\frac{28}{4}
=7
$