7x^2=18x-8

Solution for 7x^2=18x-8 equation:

7x^2=18x-8

We move all terms to the left:

7x^2-(18x-8)=0

We get rid of parentheses

7x^2-18x+8=0

a = 7; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·7·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10}{2*7}=\frac{8}{14}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10}{2*7}=\frac{28}{14}
=2
$