8x^2=38x-35

Solution for 8x^2=38x-35 equation:

8x^2=38x-35

We move all terms to the left:

8x^2-(38x-35)=0

We get rid of parentheses

8x^2-38x+35=0

a = 8; b = -38; c = +35;
Δ = b2-4ac
Δ = -382-4·8·35
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-18}{2*8}=\frac{20}{16}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+18}{2*8}=\frac{56}{16}
=3+1/2
$